Contact CR-warped product submanifolds in generalized Sasakian Space Forms
In (4) B. Y. Chen studied warped product CR-submanifolds in Kaehler manifolds. Afterward, I. Hasegawa and I. Mihai (5) obtained a sharp inequality for the squared norm of the second fundamental form for contact CR-warped products in Sasakian space form. Recently Alegre, Blair and Carriago (1) introduced generalized Sasakian space form. The aim of present paper is to study contact CR-warped product submanifolds in generalized Sasakian space form.
Geometry of Warped Product CR-Submanifolds in Kaehler Manifolds
Abstract. In this paper we study warped product CR-submanifolds in Kaehler manifolds and introduce the notion of CR-warped products. We prove several fundamental properties of CR-warped products in Kaehler manifolds and establish a general inequality for an arbitrary CR-warped product in an arbitrary Kaehler manifold. We then investigate CR-warped products in a general Kaehler manifold which satisfy the equality case of the inequality. Finally we classify CR-warped products in complex Euclidean space which satisfy the equality.
A new class of numerical sequences and its applications to sine and cosine series
First, it is proved that the class of classical quasi-monotone sequences is not comparable to the newly defined class of sequences of ‘rest bounded variation’. Considering this result, we prove three sample theorems for sequences of rest bounded variation, being analogues of the theorems proved earlier for monotone or quasi-monotone sequences. One of them gives a partial answer to a question raised by R. P. Boas Jr.