Invariant submanifolds of generalized Sasakian-space-forms. (English) Zbl 1396.53072
Summary: This paper deals with the study of invariant submanifolds of generalized Sasakian-space-forms with respect to Levi-Civita connection as well as semi-symmetric metric connection. We provide an example of such submanifolds and obtain many new results including the necessary and sufficient conditions under which the submanifolds are totally geodesic. The Ricci solitons of such submanifolds are also studied.
MSC:
| 53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
| 37J15 | Symmetries, invariants, invariant manifolds, momentum maps, reduction (MSC2010) |
| 53B25 | Local submanifolds |
| 35C08 | Soliton solutions |
Keywords:
generalized Sasakian space form; invariant submanifold; semi parallel submanifold; totally geodesic; semi-symmetric metric connection; Ricci solitonReferences:
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