Abstract
The largest class of Riemannian almost product manifolds, which is closed with respect to the group of the conformal transformations of the Riemannian metric, is the class of the conformal Riemannian P-manifolds. This class is an analogue of the class of the conformal Kähler manifolds in almost Hermitian geometry. The main aim of this work is to obtain properties of manifolds of this class with connections, whose curvature tensors have similar properties as the Kähler tensors in Hermitian geometry.
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References
Gray A., Hervella L.: The sixteen classes of almost Hermitian manifolds and their linear invariants. Ann. Mat. Pura Appl. 123, 35–58 (1980)
Gribacheva, D.: Natural connections on Riemannian product manifolds. Comput. Rend. Acad. Bulg. Sci. 64(6), 799–806 (2011)
Gribacheva, D.: A natural connection on a basic class of Riemannian product manifolds. Int. J. Geom. Methods Mod. Phys. 9(7), 1250057 (2012)
Gribacheva, D., Mekerov, D.: Natural connections on conformal Riemannian P-manifolds. Comput. Rend. Acad. Bulg. Sci. 65(5), 581–590 (2012)
Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry, vol.1. Interscience Publishers, New York (1963)
Manev, M., Ivanova, M.: Almost contact B-metric manifolds with curvature tensors of Kähler type. Plovdiv Univ. Sci. Works Math. (in Press) arXiv:1203.3290
Mekerov, D.: On Riemannian almost product manifolds with nonintegrable structure. J. Geom. 89(1–2), 119–129 (2008)
Mihova, V.: Canonical connections and the canonical conformal group on a Riemannian almost product manifold. Serdica Math. P. 15 351–358 (1989)
Naveira, A.M.: A classification of Riemannian almost product manifolds. Rend. Math. 3, 577–592 (1983)
Staikova, M.: Curvature properties of Riemannian P-manifolds. Plovdiv Univ. Sci. Works Math. 32 (3), 241–251 (1987)
Staikova, M., Gribachev, K.: Canonical connections and their conformal invariants on Riemannian P-manifolds. Serdica Math. P. 18, 150–161 (1992)
Staikova, M., Gribachev, K., Mekerov, D.: Riemannian P-manifolds of constant sectional curvatures. Serdica Math. J. 17, 212–219 (1991)
Yano, K.: Differential geometry on complex and almost complex spaces. Pure and Applied Mathematics, vol. 49. Pergamon Press Book, New York (1965)
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Dedicated to the 75th anniversary of Prof. Kostadin GRIBACHEV
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Gribacheva, D., Mekerov, D. Conformal Riemannian P-manifolds with connections whose curvature tensors are Riemannian P-tensors. J. Geom. 105, 273–286 (2014). https://doi.org/10.1007/s00022-013-0206-y
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DOI: https://doi.org/10.1007/s00022-013-0206-y