In this paper, we introduce the notion of radical transversal screen Cauchy-Riemann (SCR)- lightlike submanifolds indefinite Sasakian manifolds giving characterization theorem with some nontrivial examples such submanifolds. Integrability conditions distributions D1, D2, D and D? on SCR-lightlike an manifold have been obtained. Further, obtain necessary sufficient for foliations determined by a...

In this short note, we discuss certain examples of Legendrian submanifolds, whose linearized contact (co)homology groups over integers have non-vanishing algebraic torsion. More precisely, for a given arbitrary finitely generated abelian group [Formula: see text] and positive integer text], construct submanifolds the standard vector space text]th computed with respect to augmentation is isomorp...

For a pair of smooth transversally intersecting submanifolds in some enveloping manifold, we study the algebra generated by pseudodifferential operators and (co)boundary corresponding to submanifolds. We establish that such an has 18 types generating elements. from this algebra, define concept symbol obtain composition formula.

this article concerned on the study of signature submanifolds for curves under lie group actions se(2), sa(2) and for surfaces under se(3). signature submanifold is a regular submanifold which its coordinate components are dierential invariants of an associated manifold under lie group action, and therefore signature submanifold is a key for solving equivalence problems.

By a theorem of Mclean, the deformation space of an associative submanifold Y of an integrable G2-manifold (M, ϕ) can be identified with the kernel of a Dirac operator D / : Ω 0 (ν) → Ω 0 (ν) on the normal bundle ν of Y. Here, we generalize this to the non-integrable case, and also show that the deformation space becomes smooth after perturbing it by natural parameters, which corresponds to mov...

We give a simple proof of the Chen inequality involving invariant δ(k) submanifolds in Riemannian space forms. derive Chen’s first and Chen–Ricci inequality. Additionally, we establish corresponding for statistical submanifolds.

We consider Lagrangian Floer cohomology for a pair of Lagrangian submanifolds in a symplectic manifold M . Suppose that M carries a symplectic involution, which preserves both submanifolds. Under various topological hypotheses, we prove a localization theorem for Floer cohomology, which implies a Smith-type inequality for the Floer cohomology groups in M and its fixed point set. Two application...

In this paper we consider a dominating Finsler metric on a complete Riemannian manifold. First we prove that the energy integral of the Finsler metric satisfies the Palais-Smale condition, and ask for the number of geodesics with endpoints in two given submanifolds. Using Lusternik-Schnirelman theory of critical points we obtain some multiplicity results for the number of Finsler-geodesics betw...

In the standard contact (2n+1)-space when n > 1, we construct infinite families of pairwise non-Legendrian isotopic, Legendrian n-spheres, n-tori and surfaces which are indistinguishable using classically known invariants. When n is even these are the first known examples of non-Legendrian isotopic, Legendrian submanifolds of (2n + 1)-space. Such constructions indicate a rich theory of Legendri...

In this note, we study properties of the gradient map of the isoparametric polynomial. For a given isoparametric hypersurface in sphere, we calculate explicitly the gradient map of its isoparametric polynomial which turns out many interesting phenomenons and applications. We find that it should map not only the focal submanifolds to focal submanifolds, isoparametric hypersurfaces to isoparametr...