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NCTS Seminar in Differential Geometry
 
16:00 - 17:00, March 24, 2016 (Thursday)
Room 440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Heat Kernel Asymptotics, Index and Embedding Theorems on CR Manifolds with S1 Actions
Chin-Yu Hsiao (Academia Sinica)

Organizer
 
Yng-Ing Lee (NTU)
Kuo-Wei-Lee (NTU)
Chun-Chi Lin (NTNU)
Chung-Jun Tsai (NTU)
Mao-Pei Tsui (NTU)
 
 
Abstract
 
Among those transversally elliptic operators initiated by Atiyah
and Singer, Kohn’s b operator on CR manifolds with S1 action
is a natural one of geometric significance for complex analysts.
Our first main result establishes an asymptotic expansion for the
heat kernel of such an operator with values in its Fourier coefficients,
which involves an unprecedented contribution in terms
of a distance function from the lower dimensional stratum of the
S1-action. Our second main result computes a local index density,
in terms of tangential characteristic forms, on such manifolds including
Sasakian manifolds of interest in String Theory, by showing
that the non-trivial contributions from the stratum in the heat
kernel expansion will eventually cancel out. As applications of
our CR index theorem we can produce many CR functions on
a weakly pseudoconvex CR manifold with transversal S1 action
and many CR sections on some class of CR manifolds. We will
also discuss some embedding Theorems in CR geometry.


 

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