In this paper we analyse briefly some properties of hemi-slant sub-manifold (LCS)n-manifold. Here discuss about necessary and sufficient conditions for distributions to be integrable obtain results in direction. We also study the geometry leaves submanifold At last give an example a

Recent years have witnessed a resurgence of twistor methods in both mathematics and physics. On the physics side, this development has primarily been driven by Witten’s discovery [21] that strings in twistor space can be used to calculate Yang-Mills scattering amplitudes, resulting in concrete experimental predictions that can be tested using existing particle accelerators. Here, one of the mai...

Let M " be a smooth, closed, orientable 2«-manifold and suppose that Kx"~ is an orientable submanifold of M " dual to a cohomology class x . If d is a positive integer, the signatures of Kd"~ and K"~ are related by a numerical congruence. If n is odd, then any codimension 2 submanifold of CP" fixed by a diffeomorphism of odd prime order is dual to the generator of the cohomology algebra.

In this note we consider an arbitrary submanifold C of a Poisson manifold P and ask whether it can be embedded coisotropically in some bigger submanifold of P . We define the classes of submanifolds relevant to the question (coisotropic, Poisson-Dirac, pre-Poisson ones), present an answer to the above question and consider the corresponding picture at the level of Lie groupoids, making concrete...

Let M7 a manifold with holonomy in G2, and Y 3 an associative submanifold with boundary in a coassociative submanifold. In [5], the authors proved that MX,Y , the moduli space of its associative deformations with boundary in the fixed X, has finite virtual dimension. Using Bochner’s technique, we give a vanishing theorem that forces MX,Y to be locally smooth. MSC 2000: 53C38 (35J55, 53C21, 58J32).

We study a natural Dirac operator on a Lagrangian submanifold of a Kähler manifold. We first show that its square coincides with the Hodge de Rham Laplacian provided the complex structure identifies the Spin structures of the tangent and normal bundles of the submanifold. We then give extrinsic estimates for the eigenvalues of that operator and discuss some examples. Mathematics Subject Classif...

the problem of automatic signature recognition has received little attention incomparison with the problem of signature verification, despite its potentialapplications for many business processes and can be used effectively in paperlessoffice projects. this paper presents model-based off-line signature recognition withrotation invariant features. non-linear rotation of signature patterns is one...

For this quarter of century, differential operators in a lower dimensional submanifold embedded or immersed in real n-dimensional euclidean space E n have been studied as quantum mechanical models, which are realized as restriction of the operators in E n to the submanifold. For this decade, the Dirac operators in the submanifold have been investigated in such a scheme , which are identified wi...