1. CMB 2011 (vol 55 pp. 870)
|Left Invariant Einstein-Randers Metrics on Compact Lie Groups|
In this paper we study left invariant Einstein-Randers metrics on compact Lie groups. First, we give a method to construct left invariant non-Riemannian Einstein-Randers metrics on a compact Lie group, using the Zermelo navigation data. Then we prove that this gives a complete classification of left invariant Einstein-Randers metrics on compact simple Lie groups with the underlying Riemannian metric naturally reductive. Further, we completely determine the identity component of the group of isometries for this type of metrics on simple groups. Finally, we study some geometric properties of such metrics. In particular, we give the formulae of geodesics and flag curvature of such metrics.
Keywords:Einstein-Randers metric, compact Lie groups, geodesic, flag curvature
Categories:17B20, 22E46, 53C12
2. CMB 2004 (vol 47 pp. 354)
|An Integral Formula on Seifert Bundles |
We prove an integral formula on closed oriented manifolds equipped with a codimension two foliation whose leaves are compact.
3. CMB 2002 (vol 45 pp. 378)
|The Local MÃ¶bius Equation and Decomposition Theorems in Riemannian Geometry |
A partial differential equation, the local M\"obius equation, is introduced in Riemannian geometry which completely characterizes the local twisted product structure of a Riemannian manifold. Also the characterizations of warped product and product structures of Riemannian manifolds are made by the local M\"obius equation and an additional partial differential equation.
Keywords:submersion, MÃ¶bius equation, twisted product, warped product, product Riemannian manifolds
4. CMB 2001 (vol 44 pp. 129)
|LinÃ©arisation symplectique en dimension 2 |
In this paper the germ of neighborhood of a compact leaf in a Lagrangian foliation is symplectically classified when the compact leaf is $\bT^2$, the affine structure induced by the Lagrangian foliation on the leaf is complete, and the holonomy of $\bT^2$ in the foliation linearizes. The germ of neighborhood is classified by a function, depending on one transverse coordinate, this function is related to the affine structure of the nearly compact leaves.
Keywords:symplectic manifold, Lagrangian foliation, affine connection