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


Bejan C., Güler S.

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

  • Publication Type: Article / Article
  • Volume: 113 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.1007/s13398-018-0533-9
  • Title of Journal : REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
  • Page Numbers: pp.1173-1189

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.