S1-equivariant Minimal Tori in S4 and S1-equivariant Willmore Tori in S3.
Saddle surfaces admitting local support planes.
Scalar Curvature and Real Submanifolds of Codimension 2 of a Complex Projective Space.
Screen conformal half-lightlike submanifolds.
Second variation and stabilities of minimal lagrangian submanifolds in Kähler manifolds.
Sectional curvatures of minimal hypersurfaces immersed in
Semiparallel isometric immersions of 3-dimensional semisymmetric Riemannian manifolds
A Riemannian manifold is said to be semisymmetric if . A submanifold of Euclidean space which satisfies is called semiparallel. It is known that semiparallel submanifolds are intrinsically semisymmetric. But can every semisymmetric manifold be immersed isometrically as a semiparallel submanifold? This problem has been solved up to now only for the dimension 2, when the answer is affirmative for the positive Gaussian curvature. Among semisymmetric manifolds a special role is played by the foliated...
Semi-slant Riemannian maps into almost Hermitian manifolds
We introduce semi-slant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds as a generalization of semi-slant immersions, invariant Riemannian maps, anti-invariant Riemannian maps and slant Riemannian maps. We obtain characterizations, investigate the harmonicity of such maps and find necessary and sufficient conditions for semi-slant Riemannian maps to be totally geodesic. Then we relate the notion of semi-slant Riemannian maps to the notion of pseudo-horizontally weakly conformal...
Sharp eigenvalue estimates of closed -hypersurfaces in locally symmetric spaces
The purpose of this article is to obtain sharp estimates for the first eigenvalue of the stability operator of constant mean curvature closed hypersurfaces immersed into locally symmetric Riemannian spaces satisfying suitable curvature conditions (which includes, in particular, a Riemannian space with constant sectional curvature). As an application, we derive a nonexistence result concerning strongly stable hypersurfaces in these ambient spaces.
Simons Type Equation in and and Applications
Let be an immersed surface in with constant mean curvature. We consider the traceless Weingarten operator associated to the second fundamental form of the surface, and we introduce a tensor , related to the Abresch-Rosenberg quadratic differential form. We establish equations of Simons type for both and . By using these equations, we characterize some immersions for which or is appropriately bounded.
Simultaneous unitarizability of SL-valued maps, and constant mean curvature k-noid monodromy
We give necessary and sufficient local conditions for the simultaneous unitarizability of a set of analytic matrix maps from an analytic 1-manifold into under conjugation by a single analytic matrix map.We apply this result to the monodromy arising from an integrable partial differential equation to construct a family of -noids, genus-zero constant mean curvature surfaces with three or more ends in euclidean, spherical and hyperbolic -spaces.
Slant submanifolds in cosymplectic manifolds
We give some examples of slant submanifolds of cosymplectic manifolds. Also, we study some special slant submanifolds, called austere submanifolds, and establish a relation between minimal and anti-invariant submanifolds which is based on properties of the second fundamental form. Moreover, we give an example to illustrate our result.
Slant submanifolds with prescribed scalar curvature into cosymplectic space form.
Slant surfaces with prescribed Gaussian curvature.
Sobre inmersiones isométricas de variedades rienmmannianas en espacios euclideos.
Some 2-type submanifolds and applications
Some existence and uniqueness theorems for doubly periodic minimal surfaces.
Some inequalities for immersed surfaces.
Some nonexistence theorems on stable minimal submanifolds
We prove that there exist no stable minimal submanifolds in some n-dimensional ellipsoids, which generalizes J. Simons' result about the unit sphere and gives a partial answer to Lawson–Simons' conjecture.
Some recent developments in the theory of properly embedded minimal surfaces in