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An interesting class of submanifolds of a Kähler manifold M2n is the class of submanifolds Nn ⊑ M2n which are minimal with respect to the metric on M2n and are Lagrangian with respect to the symplectic form on M2n. A general Kähler manifold will not have any of these submanifolds. However, in this paper, we show that if the metric on M2n is also Einstein, then these minimal Lagrangian submanifolds...
In this paper, we use the precise estimate of the lower bound of Levi form of an hermitian manifold to obtain the conditions of Steinness and Liouville theorem.
Let M be an n-dimensional oriented compact and C∞ manifold, V the m-dimensional real vector bundle on M, and Pk(V) the kth Pontrjagin characteristic form of V. In this paper, we try to calculate the integral $$\int {_M P_k (V)\Lambda \sigma } $$ where σ be any closed (n-4k)-form of M. Let V⊗C be the complexification of V, $$u_C = \left\{ {s_1 + \sqrt { - 1} s_1 ^\prime ,...,s_{m - 2k} + \sqrt...
We generalize here the theorem in [1] to the case of Yang-Mills theory. The smoothing of the connection is achieved by using the evolution equation of Yang-Mills action. We obtain the Ck-bound of curvatures of new connection in terms of the Co-bound of curvatures of the original connection. As an application, we prove that the evolution ecuation has a unique solution for a maximal time interval 0≤t<T*≤∞...
These notes are intended to give an introduction to the ideas of twistor constructions for harmonic maps which are, at the present time, developing very fast. We explain the ubiquitous "J2" structure in twistor theory by showing how it naturally arises from a generalization of S.S. Chern's fundamental theorem on the antiholomorphicity of the Gauss map of a minimal immersion. We show how...
Let M be a complete Riemannian manifold with sectional curvature KM>-H>0, Bonnet's theorem tells us that the fundamental group π1(M) of M is finite. In this note, we'll determine π1(M) under some conditions on the closed geodesics in M.
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