Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

 

Transversely projective structures on a transversely holomorphic foliation, II


Author: Indranil Biswas
Journal: Conform. Geom. Dyn. 6 (2002), 61-73
MSC (2000): Primary 37F75; Secondary 53B10
Published electronically: August 7, 2002
MathSciNet review: 1948849
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2000): 37F75, 53B10

Retrieve articles in all journals with MSC (2000): 37F75, 53B10


Additional Information

Indranil Biswas
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
Email: indranil@math.tifr.res.in

DOI: http://dx.doi.org/10.1090/S1088-4173-02-00085-1
PII: S 1088-4173(02)00085-1
Received by editor(s): October 22, 2001
Received by editor(s) in revised form: June 24, 2002
Published electronically: August 7, 2002
Article copyright: © Copyright 2002 American Mathematical Society