Geodesic
Holomorphic Riemannian Maps
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2014), pp. 422-429.

Voir la notice de l'article provenant de la source Math-Net.Ru

We introduce holomorphic Riemannian maps between almost Hermitian manifolds as a generalization of holomorphic submanifolds and holomorphic submersions, give examples and obtain a geometric characterization of harmonic holomorphic Riemannian maps from almost Hermitian manifolds to Kähler manifolds. 
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B. Şahin. Holomorphic Riemannian Maps. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2014), pp. 422-429. http://geodesic.mathdoc.fr/item/JMAG_2014_10_a2/

[1] R. Abraham, J. E. Marsden, N. Ratiu, Manifolds, Tensor Analysis, and Applications, Springer-Verlag, New York, 1988 | MR

[2] P. Baird, J. C. Wood, Harmonic Morphisms between Riemannian Manifolds, Clarendon Press, Oxford, 2003 | MR

[3] P. Candelas, G. Horowitz, A. Strominger, E. Witten, “Vacuum Configurations for Superstrings”, Nucl. Phys. B, 258 (1985), 46–74 | DOI | MR

[4] G. Esposito, “From Spinor Geometry to Complex General Relativity”, Int. J. Geom. Methods Mod. Phys., 2:4 (2005), 675–731 | DOI | MR | Zbl

[5] M. Falcitelli, S. Ianus, A. M. Pastore, Riemannian Submersions and Related Topics, World Scientific Publishing Co., Inc., River Edge–New York, 2004 | MR | Zbl

[6] A. E. Fischer, “Riemannian Maps between Riemannian Manifolds”, Contemporary Math., 132, 1992, 331–366 | DOI | MR | Zbl

[7] E. Garcia-Rio, D. N. Kupeli, Semi-Riemannian Maps and their Applications, Kluwer Academic, 1999 | MR

[8] A. Gray, “Pseudo-Riemannian Almost Product Manifolds and Submersions”, J. Math. Mech., 16 (1967), 715–737 | MR | Zbl

[9] D. E. Lerner, P. D. Sommers, Complex Manifold Techniques in Theoretical Physics, Pitman Advanced Publishing, 1979 | MR | Zbl

[10] T. Nore, “Second Fundamental Form of a Map”, Ann. Mat. Pur. and Appl., 146 (1987), 281–310 | DOI | MR | Zbl

[11] B. O'Neill, “The Fundamental Equations of a Submersion”, Michigan Math. J., 13 (1966), 459–469 | DOI | MR | Zbl

[12] R. Penrose, “Physical Spacetime and Nonrealizable CR-Structure”, Proc. Simposia in Pure Math., 39, 1983, 401–422 | DOI | Zbl

[13] B. Şahin, “Invariant and Anti-Invariant Riemannian Maps to Kähler Manifolds”, Int. J. Geom. Methods Mod. Phys., 7:3 (2010), 1–19 | MR

[14] A. J. Tromba, Teichmuller Theory in Riemannian Geometry, Birkhauser Verlag, Boston, 1992 | MR | Zbl

[15] B. Watson, “Almost Hermitian Submersion”, J. Diff. Geom., 11 (1976), 147–165 | MR | Zbl

[16] K. Yano, M. Kon, Structures on Manifolds, Ser. Pure Math. World Scientific, 1984 | DOI | MR