Existence and stability of isotropic moduli spaces

Abstract

Manifolds are simplifications of our accustomednotions about curves and exteriors to arbitrary dimensional objects. Generally, A Manifolds is a topological space which is homeomorphic to ℝ . Connections of manifolds are of central importance in modern geometry in large part because they allow a comparison between the local geometry at one point and the local geometry at another point. It is a well-known fact that, a Riemannian metric on a differentiable manifold induces a Riemannian metric on its submanifold and, hence, a Riemannian connection on the manifold induces a Riemannian connection on its submanifold. We haveconcerned aboutLie groups and Lie Algebra which deals with the applications of classical mechanics, In the mathematical fields of differential geometry and tensor calculus, differential forms provide a unified approach to defining integrands over curves, surfaces, volumes, and higher-dimensional manifolds . In this paper, we established the theorem of Stability of isotropic submanifolds whereX be a compact complex submanifold of a complex manifold Y. The main object of interest in this paper is the set M of all holomorphic deformations of Xinside Y, i.e. a point t in M can be thought of as a” nearby” compact complex submanifold in Y.Instead of analyzing some particularKodaira moduli spaces (as is normally done in twister theory, where moduli spaces of rational curves and quadrics with specific normal bundles have been only considered), This generalizes the result of Merkulov on Isotropic Submanifolds, which is not necessarily on Legendre and Kodaira.