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In this paper we characterize totally umbilic hypersurfaces in a space form by a property of the extrinsic shape of circles on hypersurfaces. This characterization corresponds to characterizations of isoparametric hypersurfaces in a space form by properties of the extrinsic shape of geodesics due to Kimura-Maeda.

Characterization on Mixed Generalized Quasi-Einstein Manifold

Sampa Pahan, Buddhadev Pal, Arindam BHATTACHARYYA (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In the present paper we study characterizations of odd and even dimensional mixed generalized quasi-Einstein manifold. Next we prove that a mixed generalized quasi-Einstein manifold is a generalized quasi-Einstein manifold under a certain condition. Then we obtain three and four dimensional examples of mixed generalized quasi-Einstein manifold to ensure the existence of such manifold. Finally we establish the examples of warped product on mixed generalized quasi-Einstein manifold.

Characterizations of complex space forms by means of geodesic spheres and tubes

J. Gillard (1996)

Colloquium Mathematicae

We prove that a connected complex space form ( $M^{n}$ ,g,J) with n ≥ 4 can be characterized by the Ricci-semi-symmetry condition ${\tilde{R}}_{X Y} \cdot \tilde{ϱ} = 0$ and by the semi-parallel condition ${\tilde{R}}_{X Y} \cdot σ = 0$ , considering special choices of tangent vectors $X, Y$ to small geodesic spheres or geodesic tubes (that is, tubes about geodesics), where $\tilde{R}$ , $\tilde{ϱ}$ and $σ$ denote the Riemann curvature tensor, the corresponding Ricci tensor of type (0,2) and the second fundamental form of the spheres or tubes and where ${\tilde{R}}_{X Y}$ acts as a derivation.

Characterizations of conformally flat hypersurfaces

Johan Deprez, Piet A. Verheyen, Leopold C. A. Verstraelen (1985)

Czechoslovak Mathematical Journal

Characterizations of spacelike general helices in Lorentzian manifolds

Kazim Ilarslan (2003)

Kragujevac Journal of Mathematics

Characterizations of the nonlinear connection in the higher order geometry.

Bucataru, Ioan (1997)

Balkan Journal of Geometry and its Applications (BJGA)

Characterizations of the sphere by the curvature of the second fundamental form

Thomas Hasanis (1982)

Colloquium Mathematicae

Characterizations of the sphere in $E^{4}$ by means of the pseudoparallel mean curvature vector field

Karel Svoboda (1980)

Časopis pro pěstování matematiky

Characterizing weakly symmetric spaces as Gelfand pairs.

Nguyêñ, Hiêú (1999)

Journal of Lie Theory

Characters of the irreducible highest weight modules over the virasoro and super-virasoro algebras

Dobrev, V. K. (1987)

Proceedings of the 14th Winter School on Abstract Analysis

Charakterisierung symmetrischer R-Räume durch ihre Einheitsgitter.

Ottmar Loos (1985)

Mathematische Zeitschrift

Charles Ehresmann's concepts in differential geometry

Paulette Libermann (2007)

Banach Center Publications

We outline some of the tools C. Ehresmann introduced in Differential Geometry (fiber bundles, connections, jets, groupoids, pseudogroups). We emphasize two aspects of C. Ehresmann's works: use of Cartan notations for the theory of connections and semi-holonomic jets.

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Characterization of Riemannian Manifolds with Weak Homology Group G2 (Following A. Gray).

Characterization of some tensor concomitants of the metric tensor and vector fields under restricted groups of transformations

Characterization of the Kantor-Koecher-Tits algebra by a generalized Ahlfors operator.

Characterization of the $L^{p}$ -range of the Poisson transform in hyperbolic spaces $B (𝔽^{n})$ .

Characterization of the Pseudo-symmetries of Ideal Wintgen Submanifolds of Dimension 3

Characterization of totally umbilic hypersurfaces in a space form by circles