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C*-actions.

Andrew John Sommese, James B. Carrell (1978)

Mathematica Scandinavica

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 R ˜ X Y · ϱ ˜ = 0 and by the semi-parallel condition R ˜ X Y · σ = 0 , considering special choices of tangent vectors X , Y to small geodesic spheres or geodesic tubes (that is, tubes about geodesics), where R ˜ , 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 R ˜ X Y acts as a derivation.

Chen-Ricci inequalities for submanifolds of Riemannian and Kaehlerian product manifolds

Erol Kılıç, Mukut Mani Tripathi, Mehmet Gülbahar (2016)

Annales Polonici Mathematici

Some examples of slant submanifolds of almost product Riemannian manifolds are presented. The existence of a useful orthonormal basis in proper slant submanifolds of a Riemannian product manifold is proved. The sectional curvature, the Ricci curvature and the scalar curvature of submanifolds of locally product manifolds of almost constant curvature are obtained. Chen-Ricci inequalities involving the Ricci tensor and the squared mean curvature for submanifolds of locally product manifolds of almost...

Chen's inequality in the Lagrangian case

Teodor Oprea (2007)

Colloquium Mathematicae

In the theory of submanifolds, the following problem is fundamental: establish simple relationships between the main intrinsic invariants and the main extrinsic invariants of submanifolds. The basic relationships discovered until now are inequalities. To analyze such problems, we follow the idea of C. Udrişte that the method of constrained extremum is a natural way to prove geometric inequalities. We improve Chen's inequality which characterizes a totally real submanifold of a complex space form....

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