Lagrangian Subspaces of Manifolds
( Lagrangian Mechanics )
Publication series ： Lagrangian Mechanics
Author： Yang Liu
Publisher： IntechOpen
Publication year： 2017
E-ISBN: INT6316867290
P-ISBN(Paperback): 9789535131311
P-ISBN(Hardback): 9789535131328
Subject： TH Machinery and Instrument Industry
Keyword： Energy technology & engineering
Language： ENG
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Lagrangian Subspaces of Manifolds
Description
In this chapter, we provide an overview on the Lagrangian subspaces of manifolds, including but not limited to, linear vector spaces, Riemannian manifolds, Finsler manifolds, and so on. There are also some new results developed in this chapter, such as finding the Lagrangians of complex spaces and providing new insights on the formula for measuring length, area, and volume in integral geometry. As an application, the symplectic structure determined by the Kähler form can be used to determine the symplectic form of the complex Holmes-Thompson volumes restricted on complex lines in integral geometry of complex Finsler space. Moreover, we show that the space of oriented lines and the tangent bundle of unit sphere in Minkowski space are symplectomorphic.
Chapter