Geometry

1704 Submissions

[3] viXra:1704.0343 [pdf] submitted on 2017-04-25 13:47:47

Moduli Space of Compact Lagrangian Submanifold

Authors: Giordano Colò
Comments: 28 Pages.

We describe the deformations of moduli space M of Special Lagrangian submanifolds in the compact case and we give a characterization of the topology of M by using McLean theorem. By constructing Banach spaces on bundle sections and by elliptical operators, we are able to use Hodge theory to study the topology of the manifold. Starting from McLean results, for which moduli spaces of compact special Lagrangian submanifolds is smooth and its tangent space can be identified with harmonic 1-forms on the special Lagrangian submanifolds, we can analyze deformation theory. Then we introduce a Riemannian metric on M, from which we obtain other important properties.
Category: Geometry

[2] viXra:1704.0328 [pdf] submitted on 2017-04-25 03:20:29

Apollonius Circles of Rank -1

Authors: Ion Patrascu, Florentin Smarandache
Comments: 3 Pages.

In this article, we highlight some properties of the Apollonius circles of rank - 1 associated with a triangle.
Category: Geometry

[1] viXra:1704.0134 [pdf] submitted on 2017-04-11 04:15:20

The Homology Groups of $G_{n,m}(\mathbb{R})$

Authors: Xu Chen
Comments: 23 Pages.

In this article, we computed the homology groups of real Grassmann manifold $G_{n,m}(\mathbb{R})$ by Witten complex.
Category: Geometry