Kahler manifolds of quasi-constant holomorphic sectional curvature and generalized Sasakian space forms

Bejan, Cornelia-Livia; Güler, Sinem

doi:10.1007/s13398-018-0533-9

Kahler manifolds of quasi-constant holomorphic sectional curvature and generalized Sasakian space forms

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, vol.113, no.2, pp.1173-1189, 2019 (SCI-Expanded)

Publication Type: Article / Article
Volume: 113 Issue: 2
Publication Date: 2019
Doi Number: 10.1007/s13398-018-0533-9
Journal Name: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Page Numbers: pp.1173-1189
Istanbul Technical University Affiliated: Yes

Abstract

In the present paper, two geometric notions, namely Kahler manifolds of quasi-constant holomorphic sectional curvature and generalized Sasakian space forms, are related to each other, for the first time. Some conditions under which each of these structures induces the other one, are provided here. Several results are obtained on direct products (which are special cases of Naveira's classification), warped products or hypersurfaces of manifolds and relevant examples are included. A result of Niebergall and Ryan is generalized here. Some necessary and sufficient conditions for Einsteinian hypersurfaces are given at the end.