In this article, we prove a Legendrian Whitney trick which allows for the removal of intersections between codimension-two contact submanifolds and submanifolds, assuming such smooth cancellation is possible. This technique applied to show existence h-principle embeddings with prescribed structure.

Special Lagrangian submanifolds may be defined as those submanifolds which are both Lagrangian (an order 1 condition) and minimal (an order 2 condition). Alternatively, they are characterised as those submanifolds which are calibrated by a certain n-form (cf [HL]), so they have the remarkable property of being area minimizing. Their study have received many attention recently since connections ...

The success of multifactor analysis, such asMultilinear Principal Component Analysis (MPCA), results from its ability to decompose the characteristics of each sample vector into multiple parameters associated with multiple factors. MPCA parameterizes each factor based on the average structure of the submanifolds that are created by varying only this factor. This averaging process is based on th...

Recently, the present authors considered doubly warped product CR-submanifolds in a locally conformal Kaehler manifold and got some inequalities about the length of the second fundamental form ([14]). In this report, we obtain an inequality of the mean curvature of a doubly warped product CR-submanifold in a locally conformal Kaehler space form. Then, we consider the equality case of this inequ...

A symmetric space is a Riemannian manifold that is “symmetric” about each of its points: for each p ∈M there is an isometry σp of M such that (σp)∗ = −I on TpM . Symmetric spaces and their local versions were studied and classified by E.Cartan in the 1920’s. In 1980 D.Ferus [F2] introduced the concept of symmetric submanifolds of Euclidean space: A submanifold M of R is a symmetric submanifold ...

We consider the closed orientable hypersurfaces in a wide class of warped product manifolds, which include space forms, deSitter-Schwarzschild and Reissner-Nordström manifolds. By using an integral formula or Brendle’s Heintze-Karcher type inequality, we present some new characterizations umbilic hypersurfaces. These results can be viewed as generalizations classical Jellet-Liebmann theorem Ale...

We propose a unified computational framework for the problem of deformation and rigidity of submanifolds in a homogeneous space under geometric constraint. A notion of 1-rigidity of a submanifold under admissible deformations is introduced. It means every admissible deformation of the submanifold osculates a one parameter family of motions up to 1st order. We implement this idea to the question...

In this paper, we give global expressions of geodesics and isoparametric functions on a Randers sphere by navigation. We obtain families focal submanifolds in (S^{n}; F; d\mu_{BH}) Cartan-M\"unzner polynomials. Further more, construct some examples closed non-closed geodesics, functions, submanifolds.

We study deformations of associative submanifolds Y 3 ⊂ M of a G2 manifold M . We show that the deformation space can be perturbed to be smooth, and it can be made compact and zero dimensional by constraining it with an additional equation. This allows us to associate local invariants to associative submanifolds of M . The local equations at each associative Y are restrictions of a global equat...

By analysing supersymmetry transformations we derive new BPS equations for the D=11 fivebrane propagating in flat space that involve the world-volume three-form. The equations generalise those of 2,3,4 and 5 dimensional special Lagrangian submanifolds and are relevant for describing membranes ending on these submanifolds.