We prove a formula that expresses the Viterbo–Maslov index of a smooth strip in an oriented 2-manifold with boundary curves contained in 1-dimensional submanifolds in terms the degree function on the complement of the union of the two submanifolds.

In this article we show that every smooth closed oriented fourmanifold admits a decomposition into two submanifolds along common boundary. Each of these submanifolds is a complex manifold with pseudo-convex boundary. This imply, in particular, that every smooth closed simply-connected four-manifold is a Stein domain in the the complement of a certain contractible 2-complex.

The fundamental theorem of submanifolds is adapted to spacetimes. It is shown that the integrability conditions for the existence of submanifolds of a pseudo-Euclidean space contain the Einstein and Yang-Mills equations. preprint UnB/MAT/FM-M495 pacs 02.40 =m, 04.20.Cv, 11.10.Kk

In this paper, we prove a generalized integral inequality for submanifolds with parallel mean curvature vector in an arbitrary Riemannian manifold, and from which we obtain a pinching theorem for compact oriented submanifolds with parallel mean curvature vector in a complete simply connected pinched Riemannian manifold, which generalizes the results obtained by Alencar-do Carmo and Hong-Wei Xu.

In this paper, we investigate n-dimensional submanifolds with higher codimension in a unit sphere Sn+p(1). We obtain some rigidity results of submanifolds in Sn+p(1) with parallel mean curvature vector or with constant scalar curvature, which generalize some related rigidity results of hypersurfaces.

Part 2. Geometric theory 8. Curvature: Introduction 8.1. Three notions of curvature 8.2. Theorems 8.3. Examples 9. Curvature: Some details 9.1. The exponential representation 9.2. Diffeomorphism invariance 9.3. Curvature condition (CY ) 9.4. Two lemmas 9.5. Double fibration formulation 10. Equivalence of curvature conditions 10.1. Invariant submanifolds and deficient Lie algebras 10.2. Vanishin...

In this paper, we show that the calibrated method can also be used to detect indefinite minimal Lagrangian submanifolds in C k . We introduce the notion of indefinite special Lagrangian submanifolds in C k and generalize the well-known work of Harvey-Lawson to the indefinite case.

We extend the l2(Lp) decoupling theorem of Bourgain-Demeter to full class developable surfaces in R3. This completes l2 theory zero Gaussian curvature that lack planar (or umbilic) points. Of central interest our study is tangent surface associated moment curve.

A subset S of a Riemannian manifoldN is called extrinsically homogeneous if S is an orbit of a subgroup of the isometry group of N . In [Th], Thorbergsson proved the remarkable result that every complete, connected, full, irreducible isoparametric submanifold of a finite dimensional Euclidean space of rank at least 3 is extrinsically homogeneous. This result, combined with results of [PT1] and ...

The Poisson sigma model is a widely studied two-dimensional topological field theory. This note shows that boundary conditions for the Poisson sigma model are related to coisotropic submanifolds (a result announced in [math.QA/0309180]) and that the corresponding reduced phase space is a (possibly singular) dual pair between the reduced spaces of the given two coisotropic submanifolds. In addit...