Cihan Özgür

Hypersurfaces of an almost r-paracontact Riemannian Manifold Endowed with a Quarter Symmetric Non-metric Connection

We define a quarter symmetric non-metric connection in an almost r-paracontact Riemannian manifold and we consider invariant, non-invariant and anti-invariant hypersurfaces of an almost r-paracontact Riemannian manifold endowed with a quarter symmetric non-metric connection.

PSEUDO SYMMETRIC AND PSEUDO RICCI SYMMETRIC WARPED PRODUCT MANIFOLDS

We study pseudo symmetric (brie∞y (PS)n) and pseudo Ricci symmetric (brie∞y (PRS)n) warped product manifolds M £F N. If M is (PS)n, then we give a condition on the warping function that M is a pseudosymmetric space and N is a space of constant curvature. If M is (PRS)n, then we show that (i) N is Ricci symmetric and (ii) M is (PRS)n if and only if the tensor T deflned by (2.6) satisfles a certain condition.

GENERALIZED SASAKIAN SPACE FORMS WITH SEMI-SYMMETRIC METRIC CONNECTIONS

Abstract The aim of the present paper is to introduce generalized Sasakian space forms endowed with semi-symmetric metric connections. We obtain the existence theorem of a generalized Sasakian space form with semi-symmetric metric connection and we give some examples by using warped products endowed with semi-symmetric metric connection.

CHEN INEQUALITIES FOR SUBMANIFOLDS OF A COSYMPLECTIC SPACE FORM WITH A SEMI-SYMMETRIC METRIC CONNECTION

Abstract In this paper, we prove Chen inequalities for submanifolds of a cosymplectic space form of constant φ-sectional curvature N2m+1(c) endowed with a semisymmetric metric connection, i.e., relations between the mean curvature associated with the semi-symmetric metric connection, scalar and sectional curvatures, k-Ricci curvature and the sectional curvature of the ambient space.

Ricci curvature of submanifolds in Kenmotsu space forms

In 1999, Chen established a sharp relationship between the Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. Similar problems for submanifolds in complex space forms were studied by Matsumoto et al. In this paper, we obtain sharp relationships between the Ricci curvature and the squared mean curvature for submanifolds in Kenmotsu space forms.

Characterizations of Generalized Quasi-Einstein Manifolds

Abstract We give characterizations of generalized quasi-Einstein manifolds for both even and odd dimensions

ON QUASI-EINSTEIN WARPED PRODUCTS

Abstract We study quasi-Einstein warped product manifolds for arbitrary dimension n >3.

On Semiparallel and Weyl-semiparallel Hypersurfaces of Kaehler Manifolds

We study on semiparallel and Weyl semiparallel Sasakian hypersurfaces of Kaehler manifolds. We prove that a (2n + 1)-dimensional Sasakian hypersurface M of a (2n+2)-dimensional Kaehler manifold is semiparallel if and only if it is totally umbilical with unit mean curvature, if dimM = 3 and is a Calabi-Yau manifold, then is flat at each point of M. We also prove that such a hypersurface M is Weyl-semiparallel if and only if it is either an -Einstein manifold or semiparallel. We also investigate the extended classes of semiparallel and Weyl semiparallel Sasakian hypersurfaces of Kaehler manifolds.

On ø-quasiconformally symmetric Sasakian manifolds

Abstract We study locally and globally o-quasiconformally symmetric Sasakian manifolds. We show that a globally o-quasiconformally symmetric Sasakian manifold is globally o-symmetric. Some observations for a 3-dimensional locally o-symmetric Sasakian manifold are given. We also give an example of a 3-dimensional locally o-quasiconformally symmetric Sasakian manifold.

PINCHING THEOREMS FOR TOTALLY REAL MINIMAL SUBMANIFOLDS IN CP n

Let M be an n-dimensional totally real minimal submanifold in CPn. We prove that if M is semi-parallel and the scalar curvature τ , −(n−1)(n−2)(n+1) 2 ≤ τ ≤ 0, then M is an open part of the Clifford torus Tn ⊂ CPn. If M is semi-parallel and the scalar curvature τ , n(n − 1) ≤ τ ≤ n3−3n+2 2 , then M is an open part of the real projective space RPn. 2000 Mathematics Subject Classification. 53C42, 53C40, 53C20.