Characterization of higher-order tangent bundles.
Characterization of Low Dimensional RCD*(K, N) Spaces
In this paper,we give the characterization of metric measure spaces that satisfy synthetic lower Riemannian Ricci curvature bounds (so called RCD*(K, N) spaces) with non-empty one dimensional regular sets. In particular, we prove that the class of Ricci limit spaces with Ric ≥ K and Hausdorff dimension N and the class of RCD*(K, N) spaces coincide for N < 2 (They can be either complete intervals or circles). We will also prove a Bishop-Gromov type inequality (that is ,roughly speaking, a converse...
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 -range of the Poisson transform in hyperbolic spaces .
Characterization of the Pseudo-symmetries of Ideal Wintgen Submanifolds of Dimension 3
Characterization of totally umbilic hypersurfaces in a space form by circles
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
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
We prove that a connected complex space form (,g,J) with n ≥ 4 can be characterized by the Ricci-semi-symmetry condition and by the semi-parallel condition , considering special choices of tangent vectors to small geodesic spheres or geodesic tubes (that is, tubes about geodesics), where , and 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 acts as a derivation.
Characterizations of conformally flat hypersurfaces
Characterizations of spacelike general helices in Lorentzian manifolds
Characterizations of the nonlinear connection in the higher order geometry.
Characterizations of the sphere by the curvature of the second fundamental form
Characterizing weakly symmetric spaces as Gelfand pairs.
Charakterisierung symmetrischer R-Räume durch ihre Einheitsgitter.
Charles Ehresmann's concepts in differential geometry
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.
Cheeger-Chern-Simons classes of transversally symmetric foliations: Dependence relations and eta-invariants.
Cheeger's finiteness theorem for diffeomorphism classes of Riemannian manifolds.
Cheeger's inequality with a boundary term.