An Account on Links Between Finsler and Lorentz Geometries for Riemannian Geometers

Erreferentzia bibliografikoak

• Aké, L., Flores, J.L., Sánchez, M.: Structure of globally hyperbolic spacetimes-with-timelike-boundary. Rev. Mat. Iberoam. 37(1), 45–94 (2021)
• Alías, L.J., Romero, A., Sánchez, M.: Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes. Gen. Relativ. Gravitation 27(1), 71–84 (1995)
• Anderson, H.E.: Predicting wind-driven wild land fire size and shape. Res. Pap. INT-305, USDA Forest Service, Intermountain Forest and Range Experiment Station, Ogden (1983)
• Bao, D., Chern, S.-S., Shen, Z.: An Introduction to Riemann-Finsler geometry. In: Graduate Texts in Mathematics, vol. 200. Springer, New York (2000)
• Bao, D., Robles, C., Shen, Z.: Zermelo navigation on Riemannian manifolds. J. Differ. Geom. 66, 377–435 (2004)
• Barceló, C., Liberati, S., Visser, M.: Analogue gravity. Living Rev. Relativ. 14, 3 (2011)
• Bartolo, R., Caponio, E., Germinario, A.V., Sánchez, M.: Convex domains of Finsler and Riemannian manifolds. Calc. Var. Partial Differ. Equ. 40, 335–356 (2011)
• Beem, J.K., Ehrlich, P.E., Easley, K.L.: Global Lorentzian geometry. In: Monographs and Textbooks in Pure and Applied Mathematics, vol. 202, 2nd ed. Marcel Dekker, Inc., New York (1996)
• Bernal, A.N., Sánchez, M.: Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes. Comm. Math. Phys. 257(1), 43–50 (2005)
• Bernal, A.N., Sánchez, M.: Further results on the smoothability of Cauchy hypersurfaces and Cauchy time functions. Lett. Math. Phys. 77(2), 183–197 (2006)
• Bernal, A.N., Sánchez, M.: Globally hyperbolic spacetimes can be defined as ‘causal’ instead of ‘strongly causal’. Classical Quantum Gravity 24(3), 745–749 (2007)
• Biferale, L., Bonaccorso, F., Buzzicotti, M., Clark Di Leoni, P., Gustavsson, K.: Zermelo’s problem: optimal point-to-point navigation in 2D turbulent flows using reinforcement learning. Chaos 29(10), 103138 (2019), 13 pp.
• Biliotti, L., Javaloyes, M.A.: t-periodic light rays in conformally stationary spacetimes via Finsler geometry. Houston J. Math. 37, 127–146 (2011)
• Bonnard, B., Cots, O., Wembe, B.: A Zermelo navigation problem with a vortex singularity. ESAIM Control Optim. Calc. Var. 27(suppl. S10), 37 (2021)
• Bonnard, B., Cots, O., Gergaud, J., Wembe, B.: Abnormal geodesics in 2D-Zermelo navigation problems in the case of revolution and the fan shape of the small time balls. Systems Control Lett. 161, 105140 (2022)
• Bryson, Jr., A.E., Ho, Y.C.: Applied optimal control. Optimization, estimation, and control. Revised printing. Hemisphere Publishing Corp., Washington, distributed by Halsted Press [John Wiley & Sons, Inc.], New York (1975)
• Cabello, J., Jaramillo, J.: A functional representation of almost isometries. J. Math. Annal. Appl. 445(2), 1243–1257 (2017)
• Caponio, E., Stancarone, G.: Standard static Finsler spacetimes. Int. J. Geom. Methods Mod. Phys. 13, 1650040 (2016)
• Caponio, E., Stancarone, G.: On Finsler spacetimes with a timelike Killing vector field. Classical Quantum Gravity 35, 085007 (2018)
• Caponio, E., Javaloyes, M.A., Masiello, A.: Morse theory of causal geodesics in a stationary spacetime. Ann. Inst. H. Poincaré Anal. Non Linéaire 27, 857–876 (2010)
• Caponio, E., Javaloyes, M.A., Masiello, A.: On the energy functional on Finsler manifolds and applications to stationary spacetimes. Math. Ann. 351, 365–392 (2011)
• Caponio, E., Javaloyes, M.A., Sánchez, M.: On the interplay between Lorentzian causality and Finsler metrics of Randers type. Rev. Mat. Iberoam. 27(3), 919–952 (2011)
• Caponio, E., Javaloyes, M.A., Sánchez, M.: Wind Finslerian structures: from Zermelo’s navigation to the causality of spacetimes. To appear in Mem. Amer. Math. Soc. ArXiv e-prints, arXiv:1407.5494 [math.DG] (2014)
• Caponio, E., Germinario, A.V., Sánchez, M.: Convex regions of stationary spacetimes and Randers spaces. Applications to lensing and asymptotic flatness. J. Geom. Anal. 26(2), 791–836 (2016)
• Caponio, E., Giannoni, F., Masiello, A., Suhr, S.: Connecting and closed geodesics of a Kropina metric. Adv. Nonlin. Stud. 21, 683–695 (2021)
• Carathéodory, C.: Calculus of Variations and Partial Differential Equations of the First Order. Holden-Day Inc., San Francisco (1967)
• Cheng, J.-H., Marugame, T., Matveev, V., Montgomery, R.: Chains in CR geometry as geodesics of a Kropina metric. Adv. Math. 350, 973–999 (2019)
• Choquet-Bruhat, Y.: The Cauchy problem. In: Gravitation: An Introduction to Current Research. Wiley, New York (1962)
• Choquet-Bruhat, Y.: Introduction to General Relativity, Black Holes, and Cosmology. Oxford University Press, Oxford (2015)
• Choquet-Bruhat, Y., Geroch, R.: Global aspects of the Cauchy problem in general relativity. Commun. Math. Phys. 14, 329–335 (1969)
• Chrusciel, P.T., Friedrich, H. (eds.): The Einstein Equations and the Large Scale Behavior of Gravitational Fields. Birkhäuser, Berlin (2004)
• Daniilidis, A., Jaramillo, J., Venegas, F.: Smooth semi-Lipschitz functions and almost isometries between Finsler manifolds. J. Func. Anal. 279(8), 108662 (2020)
• Danilo, M., Torri, C., Pfeifer, C., Voicu, N. (eds.) Beyond Riemannian Geometry in Classical and Quantum Gravity. Special Issue of Universe (2022). ISSN 2218-1997
• Dehkordi, H.R.: Applications of Randers geodesics for wildfire spread modelling. Appl. Math. Model. 106, 45–59 (2022)
• Dehkordi, H.R., Saa, A.: Huygens’ envelope principle in Finsler spaces and analogue gravity. Classical Quantum Gravity 36(8), 085008 (2019)
• Eberlein, P., O’Neill, B.: Visibility manifolds. Pacific J. Math. 46, 45–109 (1973)
• Fathi, A., Siconolfi, A.: On smooth time functions. Math. Proc. Camb. Philos. Soc. 152(2), 303–339 (2012)
• Finney, M.A.: FARSITE: Fire Area Simulator-model development and evaluation. Res. Pap. RMRS-RP-4, USDA Forest Service, Rocky Mountain Research Station, Ogden, 1998 (revised 2004)
• Flores, J.L., Herrera, J., Sánchez, M.: On the final definition of the causal boundary and its relation with the conformal boundary. Adv. Theor. Math. Phys. 15, 991–1057 (2011)
• Flores, J.L., Herrera, J., Sánchez, M.: Gromov, Cauchy and causal boundaries for Riemannian, Finslerian and Lorentzian manifolds. Mem. Amer. Math. Soc. 226, 1064 (2013)
• Geroch, R.: Domain of dependence. J. Math. Phys. 11, 437–449 (1970)
• Geroch, R.P., Kronheimer, E.H., Penrose, R.: Ideal points in spacetime. Proc. Roy. Soc. Lond. A 237, 545–567 (1972)
• Gibbons, G., Herdeiro, C., Warnick, C., Werner, M.: Stationary metrics and optical Zermelo-Randers-Finsler geometry. Phys. Rev. D 79, 044022 (2009)
• Gromov, M.: Hyperbolic manifolds, groups and actions. In: Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, 1978). Annals of Mathematics Studies, vol. 97. Princeton University Press, Princeton (1981)
• Gromov, M.: Metric structures for Riemannian and non-Riemannian spaces. Progress in Mathematics, vol. 152, Birkhäuser Boston Inc., Boston (1999)
• Harris, S.: Static- and stationary-complete spacetimes: algebraic and causal structures. Classical Quantum Gravity 32, 135026 (2015)
• Herrera, J., Javaloyes, M.A.: Stationary-complete spacetimes with non-standard splittings and pre-Randers metrics. J. Geom. Phys. 163, 104120 (2021)
• Javaloyes, M.A., Lichtenfelz, L., Piccione, P.: Almost isometries of non-reversible metrics with applications to stationary spacetimes. J. Geom. Phys. 89, 38–49 (2015)
• Javaloyes, M.A., Pendás-Recondo, E.: Lightlike hypersurfaces and time-minimizing geodesics in cone structures. In: A.L. Albujer et al. (eds.), Developments in Lorentzian Geometry, Springer Proceedings in Mathematics & Statistics, vol. 389. Springer Nature Switzerland AG, Cham (2022)
• Javaloyes, M.A., Pendás-Recondo, E., Sánchez, M.: Applications of cone structures to the anisotropic rheonomic Huygens’ principle. Nonlin. Anal. 209, 112337 (2021)
• Javaloyes, M.A., Pendás-Recondo, E., Sánchez, M.: A general model for wildfire propagation with wind and slope. SIAM J. Appl. Algebra Geom. 7(2), 414–439 (2023)
• Javaloyes, M.A., Sánchez, M.: On the definition and examples of Finsler metrics. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 13(3), 813–858 (2014)
• Javaloyes, M.A., Sánchez. M.: Some criteria for wind Riemannian completeness and existence of Cauchy hypersurfaces. In: Lorentzian Geometry and Related Topics, Springer Proceedings in Mathematics & Statistics, vol. 211. Springer, Cham (2017)
• Javaloyes, M.A., Sánchez, M.: Wind Riemannian spaceforms and Randers-Kropina metrics of constant flag curvature. Eur. J. Math. 3, 1225–1244 (2017)
• Javaloyes, M.A., Sánchez, M.: On the definition and examples of cones and Finsler spacetimes. RACSAM 114, 30 (2020)
• Javaloyes, M.A., Vitório, H.: Some properties of Zermelo navigation in pseudo-Finsler metrics under an arbitrary wind. Houston J. Math. 44(4), 1147–1179 (2018)
• Kropina, V.K.: Projective two-dimensional Finsler spaces with special metric (Russian). Trudy Sem. Vektor. Tenzor. Anal. 11, 277–292 (1961)
• Levi-Civita, T.: The Absolute Differential Calculus. Blackie & Son Limited, London and Glasgow (1927)
• Levi-Civita, T.: Über Zermelo’s Luftfahrtproblem. Z. Angew. Math. Mech. 11, 314–322 (1931)
• Manià, B.: Sopra un problema di navigazione di Zermelo. Math. Ann. 113, 584–599 (1937)
• Markvorsen, S.: A Finsler geodesic spray paradigm for wildfire spread modelling. Nonlin. Anal. RWA 28, 208–228 (2016)
• Markvorsen, S.: Geodesic sprays and frozen metrics in rheonomic Lagrange manifolds. ArXiv e-prints, arXiv:1708.07350 [math.DG] (2017)
• Matveev, V.S.: Can we make a Finsler metric complete by a trivial projective change? In: Recent Trends in Lorentzian geometry, Springer Proceedings in Mathematics & Statistics, vol. 26. Springer, New York (2013)
• Minguzzi, E.: Causality theory for closed cone structures with applications. Rev. Math. Phys. 31(5), 1930001 (2019)
• Minguzzi, E., Sánchez, M.: The causal hierarchy of spacetimes. Recent Developments in Pseudo-Riemannian Geometry. ESI Lect. Math. Phys., pp. 299–358. Eur. Math. Soc., Zürich, (2008)
• Natário, J.: An Introduction to Mathematical Relativity. Latin American Mathematics Series. Springer, Cham (2021)
• O’Neill, B.: Semi-Riemannian Geometry. Pure and Applied Mathematics, vol. 103. Academic Press, Inc., New York (1983)
• Penrose, R.: Conformal treatment of infinity. In: Relativité, Groupes et Topologie (Lectures, Les Houches, 1963 Summer School of Theoret. Phys., Univ. Grenoble), Gordon and Breach, New York, 1964. Reprinted in: Gen. Relativity Gravitation 43, 901–922 (2011)
• Perlick, V.: Fermat principle in Finsler spacetimes. Gen. Relativity Gravitation 38(2), 365–380 (2006)
• Perlick, V. (ed.) Finsler Modification of Classical General Relativity. Special Issue of Universe (2020). ISSN 2218-1997
• Richards, G.D.: Elliptical growth model of forest fire fronts and its numerical solution. Int. J. Numer. Methods Engrg. 30(6), 1163–1179 (1990)
• Ringström, H.: The Cauchy Problem in General Relativity. ESI Lectures in Mathematics and Physics, European Mathematical Society (EMS), Zürich (2009)
• Serres, U.: On Zermelo-like problems: Gauss-Bonnet inequality and E. Hopf theorem. J. Dyn. Control Syst. 15(1), 99–131 (2009)
• Shen, Z.: Finsler metrics with $$\mathbf K=0$$ and $$\mathbf S=0$$. Canad. J. Math. 55, 112–132 (2003)
• Shimada, H., Sabau, S.V.: Introduction to Matsumoto metric. Nonlin. Anal. 63, 165–168 (2005)
• Tymstra, C., Bryce, R.W., Wotton, B.M., Taylor, S.W., Armitage, O.B.: Development and structure of Prometheus: the Canadian Wildland Fire Growth Simulation Model. Inf. Rep. NOR-X-417, Nat. Resour. Can., Can. For. Serv., North. For. Cent., Edmonton (2010)
• von Mises, R.: Zum Navigationsproblem der Luftfahrt. Z. Angew. Math. Mech. 11, 373–381 (1931)
• Wald, R.M.: General Relativity. The University of Chicago Press, Chicago (1984)
• Weyl, H.: Zur gravitationstheorie. Ann. Phys. 54, 117–145 (1917)
• Yoshikawa, R., Sabau, S.V.: Kropina metrics and Zermelo navigation on Riemannian manifolds. Geom. Dedicata 171, 119–148 (2014)
• Zaustinsky, E.M.: Spaces with non-symmetric distance. Mem. Am. Math. Soc. 34, 1–91 (1959)
• Zermelo, E.: Über das Navigationsproblem bei ruhender oder veränderlicher Windverteilung. Z. Angew. Math. Mech. 11, 114–124 (1931)