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Totally umbilical semi-invariant submanifolds in locally decomposable metallic Riemannian manifolds

, 2022
Mustafa Gök, Erol Kılıç
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Totally contact-umbilical semi-invariant submanifolds of a Sasakian manifold

SUT Journal of Mathematics, 2002
The main result of this paper is that a proper, non-totally contact-geodesic, totally contact-umbilical semi-invariant \(m\)-dimensional (\(m>4\)) submanifold of a Sasakian manifold, must be a generalized Hopf manifold. Let \(M\) be an \(m\)-dimensional submanifold of a \((2n+1)\)-dimensional Sasakian manifold \((N,\phi,\xi,\eta,g)\).
S.H. Kon, Tee‐How Loo
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Totally Real Pseudo-Umbilical Submanifolds of a Complex Projective Space

Tokyo Journal of Mathematics, 1997
Let \(M\) be an \(n\)-dimensional totally real submanifold of complex projective space \(\mathbb{C} P^n\) and \(\zeta\) the mean curvature vector field of \(M\). If the second fundamental form \(h\) of \(M\) satisfies \(\langle h(X, Y),\zeta\rangle= \lambda\langle X,Y\rangle\) for all tangent vectors \(X\), \(Y\) of \(M\) and for some function ...
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A Classification theorem on totally umbilical submanifolds in a cosymplectic manifold

, 2012
In the present paper, we study totally umbilical submanifolds of cosymplectic manifolds. We obtain a result on the classification of totallyumbilical contact CR-submanifolds of a cosymplectic manifold.
UDDİN, Siraj, OZEL, Cenap
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Geometric inequalities for warped product bi-slant submanifolds with a warping function. [PDF]