Results 71 to 80 of about 179 (133)
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 2004 Let \(\widetilde{M}_n(c)\) be an \(n\)-dimensional nonflat complex space form of constant holomorphic curvature \(c\) which is either a complex projective space \(\mathbb{C}P^n(c)\) or a complex hyperbolic space \(\mathbb{C}H^n(c)\). It is known that there is no totally umbilic real hypersurface in \(\widetilde{M}_n(c)\), but there exist totally \(\eta\
Itoh, Takehiro, Maeda, Sadahiro
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Totally umbilical hypersurfaces of a locally product Riemannian manifold
Kodai Mathematical Journal, 1967 It is well known that a totally umbilical hypersurface withnon-vanishing mean curvature of a Euclidean space is isometric with a sphere. Toprove this theorem we use, among others, the fact that in a Euclidean space themean curvature of a totally umbilical hypersurface is a constant.In more general Riemannian manifolds, however, there does not exist the
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Characterization of hypersurfaces in four dimensional product spaces via two different Spin^c structures [PDF]
, 2019 The Riemannian product M1(c1)×M2(c2), where Mi(ci) denotes the 2-dimensional space form of constant sectional curvature ci ∈ R, has two different Spin c structures carrying each a parallel spinor.
Nakad, Roger, Roth, Julien
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On the first eigenvalue of spacelike hypersurfaces in Lorentzian space [PDF]
, 2006 summary:In this paper we obtain a lower bound for the first Dirichlet eigenvalue of complete spacelike hypersurfaces in Lorentzian space in terms of mean curvature and the square length of the second fundamental form.
Wu, Bing-Ye
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Contact Hypersurfaces of a Bochner-Kaehler Manifold
, 2013 We have studied contact metric hypersurfaces of a Bochner-Kaehler manifold and obtained the following two results: (1) A contact metric constant mean curvature (C M C) hypersurface of a Bochner-Kaehler manifold is a (k, µ)-contact manifold, and (2) If M ...
Sharma, Ramesh, Ghosh, Amalendu
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On Almost Pseudo-Z-symmetric Manifolds [PDF]
, 2014 summary:The object of the present paper is to study almost pseudo-Z-symmetric manifolds. Some geometric properties have been studied. Next we consider conformally flat almost pseudo-Z-symmetric manifolds.
De, Uday Chand, Pal, Prajjwal
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Totally contact umbilical lightlike hypersurfaces of indefinite Sasakian manifolds
Kodai Mathematical Journal, 2008 This paper investigates totally contact umbilical lightlike hypersurfaces which are tangent to the structure vector field. Theorems on Killing distributions, geodesibility of lightlike hypersurfaces are obtained. The geometrical configuration of such lightlike hypersurfaces and its screen distributions are established.
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Space-like hypersurfaces in locally symmetric Lorentz space
, 2009 Let M be an n-dimensional space-like hypersurface in a locally symmetric Lorentz space, with n(n−1)R=κH(κ>0) and satisfying certain additional conditions on the sectional curvature.
Shichang, Shu
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A remark on compact hypersurfaces with constant mean curvature in space forms
, 2016 . In this note we characterize compact hypersurfaces of dimension n ≥ 2 with constant mean curvature H immersed in space forms of constant curvature and satisfying an optimal integral pinching condition: they are either totally umbilical or, when n ≥ 3 ...
CATINO, GIOVANNI, Giovanni Catino
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Maximum Principle for Totally Umbilical Null Hypersurfaces and Time-dependent Null Horizons
Journal of Mathematics Research, 2015 In this paper we modify the maximum principal of (Galloway, 2000) for totally geodesic null hypersurfaces by proving a geometric maximum principle which obeys mean curvature inequalities of a family of totally umbilical null hypersurfaces of a spacetime manifold (Theorem~6).
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