Vol. 42, No. 3, 1972

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
Locally holomorphic sets and the Levi form

Louis Roberts Hunt

Vol. 42 (1972), No. 3, 681–688
Abstract

Suppose we have a real k-dimensional 𝒞2 manifold M embedded in Cn. If M has a nondegenerate complex tangent bundle of positive rank at some point p M, then the vanishing or nonvanishing of the Levi form on M near p determines whether or not M is locally holomorphic at p. We show that if M is locally holomorphic at p, then the Levi form vanishes near p, the converse being a known result. In addition we prove a C R extendibility theorem for a certain case when M is 𝒞 and has a nonzero Levi form at p M.

Mathematical Subject Classification
Primary: 32F15
Milestones
Received: 7 May 1971
Revised: 29 October 1971
Published: 1 September 1972
Authors
Louis Roberts Hunt