On a Certain Class of Complex Einstein Hypersurfaces in Indefinite Complex Space Forms.
On a particular class of warped products with fibres locally isometric to generalized Cartan hypersurfaces
We prove that every generalized Cartan hypersurface satisfies the so called Roter type equation. Using this fact, we construct a particular class of generalized Robertson-Walker spacetimes.
On an inequality of Oprea for Lagrangian submanifolds
We show that a Lagrangian submanifold of a complex space form attaining equality in the inequality obtained by Oprea in [8], must be totally geodesic.
On balls and totally geodesic submanifolds
On canonical screen for lightlike submanifolds of codimension two
In this paper we study two classes of lightlike submanifolds of codimension two of semi-Riemannian manifolds, according as their radical subspaces are 1-dimensional or 2-dimensional. For a large variety of both these classes, we prove the existence of integrable canonical screen distributions subject to some reasonable geometric conditions and support the results through examples.
On certain anti-invariant submanifolds of an S-manifold
On closed timelike distributions
On contact CR-submanifolds of Sasakian manifolds.
On CR-lightlike product of an indefinite Kaehler manifold.
On Curvature Characterizations of Some Hypersurfaces in Spaces of Constant Curvature
On Deszcz symmetries of Wintgen ideal submanifolds
It was conjectured in [26] that, for all submanifolds of all real space forms , the Wintgen inequality is valid at all points of , whereby is the normalised scalar curvature of the Riemannian manifold and , respectively , are the squared mean curvature and the normalised scalar normal curvature of the submanifold in the ambient space , and this conjecture was shown there to be true whenever codimension . For a given Riemannian manifold , this inequality can be interpreted as follows:...
On geometry of curves of flags of constant type
We develop an algebraic version of Cartan’s method of equivalence or an analog of Tanaka prolongation for the (extrinsic) geometry of curves of flags of a vector space W with respect to the action of a subgroup G of GL(W). Under some natural assumptions on the subgroup G and on the flags, one can pass from the filtered objects to the corresponding graded objects and describe the construction of canonical bundles of moving frames for these curves in the language of pure linear algebra. The scope...
On Growth and Form and Geometry. I
On Hamiltonian submanifolds.
On Hypercylinders in Conformally Symmetric Manifolds
On invariant submanifolds in almost cosymplectic manifolds
On isometric immersions into complex space forms.
On Legendre curves in -Sasakian manifolds.
On minimal generic submanifolds immersed in
We give a pinching theorem for a compact minimal generic submanifold with flat normal connection immersed in an odd-dimensional sphere with standard Sasakian structure.
On minimal homothetical hypersurfaces
We give a classification of minimal homothetical hypersurfaces in an (n+1)-dimensional Euclidean space. In fact, when n ≥ 3, a minimal homothetical hypersurface is a hyperplane, a quadratic cone, a cylinder on a quadratic cone or a cylinder on a helicoid.