Abstract
Publisher Summary This chapter presents some fundamental formulas for submanifolds of a Kaehlerian manifold, and in particular for those of a complex space form, and discusses the CR-submanifolds and generic submanifolds. The chapter discusses various theorems related to CR-submanifolds. Theorem 1 is fundamental in the study of CR-submanifolds. The f -structures are studied in which a CR-submanifold and its normal bundle admit. Theorem 2 characterizes generic submanifolds with parallel f -structure of a complex space form. An integral formula of Simons' type is derived and applying it to prove Theorems 3, 4 and 5. It is clear that every real hypersurface of a Kaehlerian manifold is automatically generic submanifold. A CR-submanifold is called a “proper CR-submanifold” if it is neither a holomorphic submanifold nor an anti-invariant submanifold.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
