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arXiv · 1509.01934

Stabilities of affine Legendrian submanifolds and their moduli spaces

Kotaro Kawai
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Abstract

We introduce the notion of affine Legendrian submanifolds in Sasakian manifolds and define a canonical volume called the $ϕ$-volume as odd dimensional analogues of affine Lagrangian (totally real or purely real) geometry. Then we derive the second variation formula of the $ϕ$-volume to obtain the stability result in some $η$-Einstein Sasakian manifolds. It also implies the convexity of the $ϕ$-volume functional on the space of affine Legendrian submanifolds. Next, we introduce the notion of special affine Legendrian submanifolds in Sasaki-Einstein manifolds as a generalization of that of special Legendrian submanifolds. Then we show that the moduli space of compact connected special affine Legendrian submanifolds is a smooth Fréchet manifold.

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Kotaro Kawai. 2016-04-21. Stabilities of affine Legendrian submanifolds and their moduli spaces. https://doi.org/10.1016/j.difgeo.2016.04.001

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