A SHORT NOTE ON BIHARMONIC SUBMANIFOLDS IN 3-DIMENSIONAL GENERALIZED (𝜅, 𝜇)-MANIFOLDS

Title & Authors
A SHORT NOTE ON BIHARMONIC SUBMANIFOLDS IN 3-DIMENSIONAL GENERALIZED (𝜅, 𝜇)-MANIFOLDS
Sasahara, Toru;

Abstract
We characterize proper biharmonic anti-invariant surfaces in 3-dimensional generalized ($\small{{\kappa}}$, $\small{{\mu}}$)-manifolds with constant mean curvature by means of the scalar curvature of the ambient space and the mean curvature. In addition, we give a method for constructing infinity many examples of proper biharmonic submanifolds in a certain 3-dimensional generalized ($\small{{\kappa}}$, $\small{{\mu}}$)-manifold. Moreover, we determine 3-dimensional generalized ($\small{{\kappa}}$, $\small{{\mu}}$)-manifolds which admit a certain kind of proper biharmonic foliation.
Keywords
biharmonic submanifolds;Legendre curves;anti-invariant surfaces;generalized ($\small{{\kappa}}$, $\small{{\mu}}$)-manifolds;
Language
English
Cited by
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