最小马斯洛夫数r -空间通常嵌入Einstein-Kähler c -空间

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2019-01-01 DOI:10.1515/coma-2019-0016

Y. Ohnita

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引用次数: 1

摘要

摘要R空间是作为黎曼对称空间的各向同性表示的轨道得到的紧致齐次空间。众所周知，每个R空间都有作为实形式的正则嵌入到Kähler C空间中，因此是一个紧嵌入的全测地拉格朗日子流形。辛流形中拉格朗日子流形的最小Maslov数是Hamiltonian同构下的不变量之一，是研究拉格朗日子流形交的Floer同调的基础。本文给出了Einstein-Kähler C空间中正则嵌入的R空间的最小Maslov数的一个李理论公式，并给出了用该公式计算的一些例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Minimal Maslov number of R-spaces canonically embedded in Einstein-Kähler C-spaces

Abstract An R-space is a compact homogeneous space obtained as an orbit of the isotropy representation of a Riemannian symmetric space. It is known that each R-space has the canonical embedding into a Kähler C-space as a real form, and thus a compact embedded totally geodesic Lagrangian submanifold. The minimal Maslov number of Lagrangian submanifolds in symplectic manifolds is one of invariants under Hamiltonian isotopies and very fundamental to study the Floer homology for intersections of Lagrangian submanifolds. In this paper we show a Lie theoretic formula for the minimal Maslov number of R-spaces canonically embedded in Einstein-Kähler C-spaces, and provide some examples of the calculation by the formula.

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来源期刊

Complex Manifolds MATHEMATICS-

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

25 weeks

期刊介绍： Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.