Keywords: Riemannian almost product structure
@article{VNGU_2016_16_4_a0,
author = {I. A. Alexandrova and S. E. Stepanov and I. I. Tsyganok},
title = {Liouville-type theorems for the theories of {Riemannian} almost product structures and submersions},
journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
pages = {3--12},
year = {2016},
volume = {16},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VNGU_2016_16_4_a0/}
}
TY - JOUR AU - I. A. Alexandrova AU - S. E. Stepanov AU - I. I. Tsyganok TI - Liouville-type theorems for the theories of Riemannian almost product structures and submersions JO - Sibirskij žurnal čistoj i prikladnoj matematiki PY - 2016 SP - 3 EP - 12 VL - 16 IS - 4 UR - http://geodesic.mathdoc.fr/item/VNGU_2016_16_4_a0/ LA - ru ID - VNGU_2016_16_4_a0 ER -
%0 Journal Article %A I. A. Alexandrova %A S. E. Stepanov %A I. I. Tsyganok %T Liouville-type theorems for the theories of Riemannian almost product structures and submersions %J Sibirskij žurnal čistoj i prikladnoj matematiki %D 2016 %P 3-12 %V 16 %N 4 %U http://geodesic.mathdoc.fr/item/VNGU_2016_16_4_a0/ %G ru %F VNGU_2016_16_4_a0
I. A. Alexandrova; S. E. Stepanov; I. I. Tsyganok. Liouville-type theorems for the theories of Riemannian almost product structures and submersions. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 16 (2016) no. 4, pp. 3-12. http://geodesic.mathdoc.fr/item/VNGU_2016_16_4_a0/
[1] Wu H. H., The Bochner Technique in Differential Geometry, Harwood Acad. Publ., Harwood, 1987
[2] Pigola S., Rigoli M., Setti A. G., Vanishing and Finiteness Results in Geometric Analysis. A Generalization of the Bochner Technique, Birkhauser Verlag AG, Berlin, 2008
[3] Sh. Koboyashi, K. Nomizu, Foundations of Differential Geometry, v. 1, Interscience Publisher, N. Y.–London, 1981
[4] Yau S. T., “Some Function-Theoretic Properties of Complete Riemannian Manifold and their Application to Geometry”, Indiana Univ. Math. J., 25:7 (1976), 659–670 | DOI
[5] Caminha A., Souza P., Camargo F., “Complete Foliations of Space Forms by Hypersurfaces”, Bull. of the Brazilian Math. Soc. New Series, 41:3 (2010), 339–353 | DOI
[6] Caminha A., “The Geometry of Closed Conformal Vector Fields on Riemannian Spaces”, Bull. of the Brazilian Math. Soc. New Series, 42:2 (2011), 277–300 | DOI
[7] Stepanov S. E., “An Integral Formula for a Riemannian Almost-Product Manifold”, Tensor, New Series, 55 (1994), 209–214
[8] S. E. Stepanov, “An integral formula for a compact manifold with a Riemannian almost product structure”, Russian Math., 38:7 (1994), 66–70
[9] S. E. Stepanov, “Geometry of projective submersions of Riemannian manifolds”, Russian Math., 43:9 (1999), 44–50
[10] S. E. Stepanov, “On the global theory of projective mappings”, Math. Notes, 58:1 (1995), 752–756 | DOI
[11] S. E. Stepanov, “$O(n)\times O(m-n)$-structures on $m$-dimensional manifolds, and submersions of Riemannian manifols”, St. Petersburg Math. J., 7:6 (1996), 1005–1016
[12] I. A. Alexandrova, J. Mikeš, S. E. Stepanov, I. I. Tsyganok, “Theorems of Liuville types in theory mappings of the complete Riemannian manifolds”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 15:3 (2015), 3–10 (in Russian)
[13] M. M. Postnikov, Lectures on Geometry, IV: Differential Geometry, Nauka, M., 1988 (in Russian)
[14] Montesinos A., “On Certain Classes of Almost Product Structures”, Michigan Math. J., 30:1 (1983), 31–36 | DOI
[15] Reinhart B. L., Differential Geometry of Foliations, Springer-Verlag, Berlin–N.Y., 1983
[16] A. Besse, Einstein Manifolds, Springer-Verlag, Berlin–Heidelberg, 1987
[17] Walczak P., Luzynczyk M., “New Integral Formulae for Two Complementary Or-Thogonal Distributions on Riemannian Manifolds”, Ann. Glob. Anal. Geom., 48:2 (2015), 195–209 | DOI
[18] Hangan T., “On Totally Geodesic Distributions of Planes”, Coll. Math. Soc. Janos Bolyai, 46 (1988), 519–530
[19] M. A. Akivis, “Flat hyperdistributions in $P^n$”, Math. Notes, 36:2 (1984), 599–604 | DOI
[20] Ponge R., Reckziegel H., “Twisted Product in Pseudo-Riemannian Geometry”, Geom. Dedic., 48:1 (1993), 15–25 | DOI
[21] S. E. Stepanov, “One class of Riemannian almost-product structures”, Sov. Math., 33:7 (1989), 51–59
[22] Grigor'yan A., Heat Kernel and Analysis on Manifolds, AMS/IP Studies in Advanced Mathematics, 47, 2009
[23] D. Gromoll, W. Meyer, W. Klingenberg, Riemannsche Geometrie im Groben, Springer-Verlag, Berlin, 1968
[24] O'Neil B., “The Fundamental Equations of a Submersion”, The Michigan Math. J., 13:4 (1966), 459–469 | DOI
[25] R. Zulanke, P. Vintgen, Differential Geometry and Vector Bundles, Nauka, M., 1975 (in Russian)
[26] Nore T., “Second Fundamental Form of a Map”, Ann. Mat. Pura ed Appl., 146 (1987), 281–310 | DOI
[27] S. E. Stepanov, “Weyl submersions”, Russian Math., 36:5 (1992), 87–89
[28] Pro C., Wilhelm F., “Riemannian Submersions Need not Preserve Positive Ricci Curvature”, Proc. of the American Math. Soc., 142:7 (2014), 2529–2535 | DOI
[29] Ishihara T., “A Mapping of Riemannian Manifolds Which Preserves Harmonic Functions”, J. Math. Kyoto Uni., 19:2 (1979), 215–229 | DOI