A certain complete space-like hypersurface in Lorentz manifolds.
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Kim, Hyang Sook, Kim, Young-Mi (2004)
Balkan Journal of Geometry and its Applications (BJGA)
Ledger, A.J., Papantoniou, B.J. (1989)
International Journal of Mathematics and Mathematical Sciences
Mayuko Kon (2008)
Czechoslovak Mathematical Journal
We give a characterization of totally -umbilical real hypersurfaces and ruled real hypersurfaces of a complex space form in terms of totally umbilical condition for the holomorphic distribution on real hypersurfaces. We prove that if the shape operator of a real hypersurface of a complex space form , , , satisfies for any , being a function, where is the holomorphic distribution on , then is a totally -umbilical real hypersurface or locally congruent to a ruled real hypersurface....
Yaning Wang (2016)
Open Mathematics
Let M3 be a three-dimensional almost Kenmotsu manifold satisfying ▽ξh = 0. In this paper, we prove that the curvature tensor of M3 is harmonic if and only if M3 is locally isometric to either the hyperbolic space ℍ3(-1) or the Riemannian product ℍ2(−4) × ℝ. This generalizes a recent result obtained by [Wang Y., Three-dimensional locally symmetric almost Kenmotsu manifolds, Ann. Polon. Math., 2016, 116, 79-86] and [Cho J.T., Local symmetry on almost Kenmotsu three-manifolds, Hokkaido Math. J., 2016,...
Poroşniuc, Dumitru Daniel (2004)
Balkan Journal of Geometry and its Applications (BJGA)
Gouli-Andreou, F., Xenos, Ph.J. (2002)
Beiträge zur Algebra und Geometrie
Mancho Manev, Miroslava Ivanova (2014)
Open Mathematics
The space of the torsion (0,3)-tensors of the linear connections on almost contact manifolds with B-metric is decomposed in 15 orthogonal and invariant subspaces with respect to the action of the structure group. Three known connections, preserving the structure, are characterized regarding this classification.
Yunhee Euh, Jeong Hyeong Park, Kouei Sekigawa (2017)
Czechoslovak Mathematical Journal
We derive a curvature identity that holds on any 6-dimensional Riemannian manifold, from the Chern-Gauss-Bonnet theorem for a 6-dimensional closed Riemannian manifold. Moreover, some applications of the curvature identity are given. We also define a generalization of harmonic manifolds to study the Lichnerowicz conjecture for a harmonic manifold “a harmonic manifold is locally symmetric” and provide another proof of the Lichnerowicz conjecture refined by Ledger for the 4-dimensional case under a...
Svetlov, A.V. (2002)
Sibirskij Matematicheskij Zhurnal
Dario Di Pinto, Antonio Lotta (2023)
Archivum Mathematicum
We prove a Frankel type theorem for submanifolds of Sasakian manifolds, under suitable hypotheses on the index of the scalar Levi forms determined by normal directions. From this theorem we derive some topological information about submanifolds of Sasakian space forms.
Masafumi Okumura (2003)
Publications de l'Institut Mathématique
Maria Luzia Leite, I.D. de Miatello (1980)
Mathematische Zeitschrift
Oproiu, Vasile (2001)
International Journal of Mathematics and Mathematical Sciences
Poroşniuc, Dumitru Daniel (2004)
Balkan Journal of Geometry and its Applications (BJGA)
Oproiu, Vasile (1999)
Beiträge zur Algebra und Geometrie
Fernández, Marisa (1987)
Portugaliae mathematica
Faen Wu, Xinnuan Zhao (2012)
Communications in Mathematics
In this paper, we give a new variational characterization of certain 4-manifolds. More precisely, let and denote the scalar curvature and Ricci curvature respectively of a Riemannian metric, we prove that if is compact and locally conformally flat and is the critical point of the functional where
Olivier Biquard, Rafe Mazzeo (2011)
Journal of the European Mathematical Society
We consider the Einstein deformations of the reducible rank two symmetric spaces of noncompact type. If is the product of any two real, complex, quaternionic or octonionic hyperbolic spaces, we prove that the family of nearby Einstein metrics is parametrized by certain new geometric structures on the Furstenberg boundary of .
Roberto Catenacci, Annalisa Marzuoli (1984)
Annales de l'I.H.P. Physique théorique
Tripathi, Mukut Mani, Kim, Jeong-Sik, Kim, Seon-Bu (2003)
International Journal of Mathematics and Mathematical Sciences
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