We generalize Khintchine’s method of constructing totally irrational singular vectors and linear forms. The main result the paper shows existence forms with large uniform Diophantine exponents on certain subsets ℝn, in particular any analytic submanifold ℝn dimension ≥2 which is not contained a proper rational affine subspace.

We set the goal to study properties of invariant submanifolds hyperbolic Sasakian manifolds. It is proven that a three-dimensional submanifold manifold totally geodesic if and only it invariant. Also, we discuss ?-Ricci-Bourguignon solitons on Finally, construct non-trivial example five-dimensional validate some our results.

The purpose of this paper is to study the second fundamental form of some submanifolds M in Euclidean spaces E" which have flat normal connection. As such, Theorem gives precise expressions for the (essentially 2) Weingarten maps of all 4-dimensional Emstem submanifolds in E6, which are specialized in Corollary 2 to the Rcciflat submanifolds. The main part ofthis paper deals with fiat submanifo...

A visible action on a complex manifold is a holomorphic action that admits a J -transversal totally real submanifold S. It is said to be strongly visible if there exists an orbit-preserving anti-holomorphic diffeomorphism σ such that σ|S = id. In this paper, we prove that for any Hermitian symmetric space D = G/K the action of any symmetric subgroup H is strongly visible. The proof is carried o...

We show that a minimal disk satisfying the free boundary condition in a constant curvature ball of any dimension is totally geodesic. We weaken the condition to parallel mean curvature vector in which case we show that the disk lies in a three dimensional constant curvature submanifold and is totally umbilic. These results extend to higher dimensions earlier three dimensional work of J. C. C. N...

A C∞ function f on a riemannian manifold M is convex provided its hessian (second covariant differential) is positive semidefinite, or equivalently if (f ◦σ)′′ ≥ 0 for every geodesic inM . We shall apply this notion in a variety of ways to the study of manifolds of negative or nonpositive curvature. Convexity has, of course, long been associated with negative curvature, but convex function seem...

In this article, we study the smoothness of Riemannian submersions for open manifolds with non-negative sectional curvature. Suppose thatM is a C-smooth, complete and non-compact Riemannian manifold with nonnegative sectional curvature. Cheeger-Gromoll [ChG] established a fundamental theory for such a manifold. Among other things, they showed that M admits a totally convex exhaustion {Ωu}u≥0 of...

We assign to each nondegenerate Hamiltonian on a closed symplectic manifold a Floer-theoretic quantity called its “boundary depth,” and establish basic results about how the boundary depths of different Hamiltonians are related. As applications, we prove that certain Hamiltonian symplectomorphisms supported in displaceable subsets have infinitely many nontrivial geometrically distinct periodic ...

In this paper, we study the geometry of a semi-Riemannian manifold M̄ of quasi-constant curvature. The main result is two characterization theorems for M̄ endowed with a statical, screen homothetic or screen totally umbilical half lightlike submanifold M . Mathematics Subject Classification: 53C25, 53C40, 53C50

The class of generic submanifold includes all real hypersurfaces, complex submanifolds, totally real submanifolds, and CR-submanifolds. In this paper we initiate the study of generic submanifolds in a nearly Kaehler manifold from differential geometric point of view. Some fundamental results in this paper will be obtained.