Harmonic morphisms between degenerate semi-riemannian manifolds

Beitrage zur Algebra und Geometrie

Volumn 46, Issue 1, 2005, Pages 261-281

  Pambira, Alberto ^a  

^a NONE

Author keywords

Degenerate semi riemannian manifold; Harmonic map; Harmonic morphism; Stationary manifold

Indexed keywords

EID: 20744434411     PISSN: 01384821     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. Baird, P.; Wood, J. C.: Harmonic morphisms between Riemannian manifolds. London Math. Soc. Monogr. New Series 29, Oxford Univ. Press, Oxford 2003. Zbl pre02019737
2. Bengtsson, I.: Degenerate metrics and an empty black hole. Classical Quantum Gravity 8 (1991), 1847-1857. Zbl 0739.53059
3. Boothby, W. M.: An introduction to differentiable manifolds and Riemannian geometry. (2nd. ed.), Pure and Applied Math. 120, Academic Press, 1986. Zbl 0596.53001
4. Cabral, L. A.; Rivelles, V. O.: Particles and strings in degenerate metric spaces. Classical Quantum Gravity 17 (2000), 1577-1594. Zbl 0949.83069
5. Crampin, M.: On differentiable manifolds with degenerate metrics. Proc. Camb. Phil. Soc. 64 (1968), 307-316. Zbl 0159.51002
6. Duggal, K. L.; Bejancu, A.: Lightlike submanifolds of semi-Riemannian manifolds and applications. Mathematics and its Applications 364, Kluwer, Dordrecht 1996. Zbl 0848.53001
7. Eells, J.; Lemaire, L.: Selected topics in harmonic maps. Reg. Conf. Ser. in Math. 50, Am. Math. Soc., Providence, Rhode Island 1983. Zbl 0515.58011
8. Fuglede, B.: Harmonic morphisms between Riemannian manifolds. Ann. Inst. Fourier, Grenoble 28(2) (1978), 107-144. Zbl 0339.53026
9. Fuglede, B.: Harmonic morphisms between semi-Riemannian manifolds. Ann. Acad. Sci. Fenn. Math. 21 (1996), 31-50. Zbl 0847.53013
10. Gratus, J.: Classical and quantum implications of the casuality structure of two-dimensional space-times with degenerate metrics. J. Math. Phys. 37(12) (1996), 6018-6032. Zbl 0863.53067
11. Gudmundsson, S.: The bibliography of harmonic morphisms. Web address: http://www.matematik.lu.se/matematiklu/personal/sigma/harmonic/bibliography.html
12. Gudmundsson, S.; Loubeau, E.; Montaldo, S.: The atlas of harmonic morphisms. http://www.matematik.lu.se/matematiklu/personal/sigma/harmonic/atlas.html
13. Ishihara, T.: A mapping of Riemannian manifolds which preserves harmonic functions. J. Math. Kyoto Univ. 19(2) (1979), 215-229. Zbl 0421.31006
14. Kupeli, D. N.: Singular semi-Riemannian geometry. Mathematics and its Applications 366, Kluwer, Dordrecht 1996. Zbl 0871.53001
15. Moisil, G. C.: Sur les géodésiques des espaces de Riemann singuliers. Bull. Math. Soc. Roumaine Sci. 42 (1940), 33-52. JFM 66.0871.01
16. Molino, P.: Riemannian foliations. Progr. in Math. 73, Birkhäuser, Basel, Boston 1988. Zbl 0633.53001
17. O'Neill, B.: Semi-Riemannian geometry (with applications to relativity). Pure Appl. Math. 103, Academic Press, New York 1983. Zbl 0531.53051
18. Pambira, A.: Harmonic maps and morphisms in semi-Riemannian and complex-Riemannian geometry. Ph.D. Thesis, University of Leeds 2002.
19. Searight, T. P.: On degenerate metrics and electromagnetism. Gen. Relativ. Gravitation 35(5) (2003), 791-805. Zbl 1015.83035
20. Strubecker, K.: Differentialgeometrie des isotropen Raumes, I. Theorie der Raumkurven. Akad. Wiss. Wien 150 (1941), 1-53. Zbl 0026.08102
21. 2. Math. Z. 47 (1942), 743-777. Zbl 0026.26301
22. Strubecker, K.: Differentialgeometrie des isotropen Raumes, III. Flächentheorie. Math. Z. 48 (1942), 369-427. Zbl 0027.25301
23. Strubecker, K.: Differentialgeometrie des isotropen Raumes, IV. Theorie der flächentreuen Abbildungen der Ebene. Math. Z. 50 (1944), 1-92. Zbl 0063.07216
24. Sulik, K.: A note on degenerate pseudo-Riemannian manifolds. Zesz. Nauk. Univ. Jagellon. 661, Pr. Mat. 24 (1984), 67-75. Zbl 0558.53024
25. Thrall, R. M.; Tornheim, L.: Vector spaces and matrices. John Wiley and sons, New York 1957. Zbl 0077.02002
26. Vogel, W. O.: Über lineare Zusammennhänge in singulären Riemannschen Räumen. Arch. Math. 16 (1965), 106-116. Zbl 0125.39401
27. Vogel, W. O.: S-metrische Zusammenhänge in isotropen Mannigfaltigkeiten. Math. Pannonica 3(2) (1992), 29-41. Zbl 0772.53008
28. Vranceanu, G.: Sur les invariants des espaces de Riemann singuliers. Disqu. math. phys. Bucareşti 2 (1942), 253-281. JFM 68.0441.03