Adiabatic limits and vanishing theorems on foliations

Details Adiabatic limits and vanishing theorems on foliations Adiabatic limits and vanishing theorems on foliations

2012-04-10

arxiv.org/abs/1204.2224v1

Mathematics

Differential Geometry

53 pages

Scientific paper

We present a direct geometric proof of the Connes vanishing theorem, which
generalizes the Lichnerowicz vanishing theorem to the case of foliations,
without using any noncommutative geometry. We also establish several new
foliation generalizations of the Lichnerowicz theorem. Moreover, we show that
there is no foliation of positive leafwise scalar curvature on any torus.

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