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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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Transversely projective structures on a transversely holomorphic foliation, II
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by Indranil Biswas PDF
Conform. Geom. Dyn. 6 (2002), 61-73 Request permission

Abstract:

Given a transversely projective foliation $\mathcal F$ on a $C^\infty$ manifold $M$ and a nonnegative integer $k$, a transversal differential operator ${\mathcal D}_{\mathcal F}(2k+1)$ of order $2k+1$ from $N^{\otimes k}$ to $N^{\otimes (-k-1)}$ is constructed, where $N$ denotes the normal bundle for the foliation. There is a natural homomorphism from the space of all infinitesimal deformations of the transversely projective foliation $\mathcal F$ to the first cohomology of the locally constant sheaf over $M$ defined by the kernel of the operator ${\mathcal D}_{\mathcal F}(3)$. On the other hand, from this first cohomology there is a homomorphism to the first cohomology of the sheaf of holomorphic sections of $N$. The composition of these two homomorphisms coincide with the infinitesimal version of the forgetful map that sends a transversely projective foliation to the underlying transversely holomorphic foliation.
References
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Additional Information
  • Indranil Biswas
  • Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
  • MR Author ID: 340073
  • Email: indranil@math.tifr.res.in
  • Received by editor(s): October 22, 2001
  • Received by editor(s) in revised form: June 24, 2002
  • Published electronically: August 7, 2002
  • © Copyright 2002 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 6 (2002), 61-73
  • MSC (2000): Primary 37F75; Secondary 53B10
  • DOI: https://doi.org/10.1090/S1088-4173-02-00085-1
  • MathSciNet review: 1948849