Special Lagrangian submanifolds of complex Euclidean space C have been studied widely over the last few years. These submanifolds are volume minimizing and, in particular, they are minimal submanifolds. When n = 2, special Lagrangian surfaces of C are exactly complex surfaces with respect to another orthogonal complex structure on R ≡ C. A very important problem here, and even a good starting p...

The purpose of this paper is to study the second fundamental form of some submanifolds M in Euclidean spaces E" which have flat normal connection. As such, Theorem gives precise expressions for the (essentially 2) Weingarten maps of all 4-dimensional Emstem submanifolds in E6, which are specialized in Corollary 2 to the Rcciflat submanifolds. The main part ofthis paper deals with fiat submanifo...

This paper aims to present work on contact pseudo-slant submanifolds of Para-Sasakian manifold. The study includes the definitions and some results type 1, 2, 3 submanifolds.

We obtain new restrictions on Maslov classes of monotone Lagrangian submanifolds $\mathbb{C}^n$. also construct families examples submanifolds, which show that the are sharp in certain cases.

The second variation operator of minimal submanifolds of Riemannian manifolds (the Jacobi operator) carries information about stability properties of the submanifold when it is thought of as a critical point for the area functional. When the ambient Riemannian manifold is a sphere S, Simons [S] characterized the totally geodesic submanifolds as the minimal submanifolds of S either with the lowe...

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(ν) → Ω(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 moving Y t...

Roughly speaking, an ideal immersion of a Riemannian manifold into a space form is an isometric immersion which produces the least possible amount of tension from the ambient space at each point of the submanifold. Recently, B.-Y. Chen studied Lagrangian submanifolds in complex space forms which are ideal. He proved that such submanifolds are minimal. He also classified ideal Lagrangian submani...

We consider the decomposition of a compact-type symmetric space into a product of factors and show that the rank-one factors, when considered as totally geodesic submanifolds of the space, are isolated from inequivalent minimal submanifolds.

We classify biharmonic submanifolds with certain geometric properties in Euclidean spheres. For codimension 1, we determine the biharmonic hypersurfaces with at most two distinct principal curvatures and the conformally flat biharmonic hypersurfaces. We obtain some rigidity results for pseudo-umbilical biharmonic submanifolds of codimension 2 and for biharmonic surfaces with parallel mean curva...