Im Rahmen des Oberseminars Analysis/Numerik spricht
Herr Brice Flamencourt (Universität Stuttgart)
Titel: „Cauchy spinors on 3-manifolds“
Abstract:
The so-called Cauchy spinors arise naturally when one considers the restriction of a parallel spinor on a spin-manifold 
to an oriented hypersurface 
of . The covariant derivative of such a restriction in the direction of 
is given by the Clifford multiplication by 
where A is the second fundamental form of the hypersurface. More generally, we can investigate the spinors satisfying this last condition on a manifold , 
being an arbitrary symmetric endomorphism field. They are called Cauchy spinors.
In dimension three, the study of Cauchy spinors on simply connected manifolds can be reduced to an equation on the endomorphism field . Since this is a non-linear differential equation, it is still hard to fully understand the structure of this spinors space, even in the simple case of the round sphere 
. However, we can give some classification results on manifolds with positive curvature. Moreover, we can use the Lie group structure of in order to make explicit computations.
Der Vortrag findet statt am:
Donnerstag, den 09.03.2023 von 14.15 - 15.15 Uhr, Raum W1 0-006
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