Submanifolds of generalized 
                
                  
                
                $$(k,\mu )$$
                
                  
                    
                      (
                      k
                      ,
                      μ
                      )
                    
                  
                
              -space-forms

In this paper, we study conformal Ricci solitons and conformal gradient Ricci solitons on generalized [Formula: see text]-space forms. The conditions for the solitons to be shrinking, steady and expanding are derived in terms of conformal pressure [Formula: see text]. We show under what conditions a Ricci semi-symmetric generalized [Formula: see text]-space form equipped with a conformal Ricci soliton forms an Einstein manifold.

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Some characterizations of anti-invariant submanifolds of trans-sasakian manifolds

Sarkar

Bhakta

Sen³

2021

Asian-European J. Math.

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The object of this paper is to study anti-invariant submanifolds of trans-Sasakian manifolds. We characterize such submanifolds on the basis of parallelism, semi-parallelism and pseudo parallelism of the second fundamental form of the submanifolds. We also characterize totally umbilical anti-invariant submanifolds of trans-Sasakian manifolds. Existence of Legendre curves on such submanifolds has been analyzed. Whether an anti-invariant submanifold of a trans-Sasakian manifold inherits local symmetry from ambient space is investigated here. Nature of Ricci soliton on anti-invariant submanifolds of trans-Sasakian manifolds has been characterized.

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Submanifolds of generalized $$(k,\mu )$$ ( k , μ ) -space-forms

Cited by 5 publications

References 15 publications

Classification of Casorati ideal Legendrian submanifolds in Sasakian space forms

Classification of Casorati ideal Legendrian submanifolds in Sasakian space forms

Conformal Ricci solitons on generalized (κ,μ)-space forms

Some characterizations of anti-invariant submanifolds of trans-sasakian manifolds

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