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We classify 4-dimensional austere submanifolds in Euclidean space ruled by 2-planes. The algebraic possibilities for second fundamental forms of an austere 4-fold M were classified by Bryant, falling...
Dirac method and symplectic submanifolds in the cotangent bundle of a factorizable Lie group
Dirac method symplectic submanifolds cotangent bundle factorizable Lie group
2010/11/18
In this work we study some symplectic submanifolds in the cotangent bundle of a factorizable Lie group defined by second class constraints. By applying the Dirac method, we study many issues of these...
Intersections of intrinsic submanifolds in the Heisenberg group
Heisenberg group intrinsic regular surfaces implicit function theorem
2010/12/14
In the first Heisenberg group, we show that the intersection of two intrinsic submanifolds with linearly independent horizontal normals locally coincides with the image of an injective continuous curv...
Shape Operator AH for Slant Submanifolds in Generalized Complex Space Forms
Shape operator slant submanifolds generalized complex space form k-Ricci curvature
2010/2/26
In this article, we establish an inequality between the sectional curvature function K and the shape operator AH at the mean curvature vector for slant submanifolds in generalized complex space forms....
On QR-Submanifolds of a Quaternionic Space form
Quaternion Kaehler Manifold QR-Submanifold Pseudo-Umbilical Submanifold Mixed Geodesic QR-Submanifold Almost Contact 3-Structure
2010/3/1
In this paper, we investigate mixed QR-submanifolds in a quaternionic space form and pseudo umbilical QR-submanifold of a quaternionic space form under some additional condition. Finally we give a nec...
QR-Submanifolds and Almost Contact 3-Structure
Quaternion Kaehler Manifold QR-Submanifold Almost Contact 3-Structure
2010/3/1
In this paper,QR-submanifolds of quaternion Kaehlerian manifolds with \dim n \perp =1 has been considered. It is shown that each QR-submanifold of quaternion Kaehlerian manifold with \dim n \perp =1 i...