✦ LIBER ✦
Generalization of Kähler angle and integral geometry in complex projective spaces II
✍ Scribed by Hiroyuki Tasaki
- Publisher
- John Wiley and Sons
- Year
- 2003
- Tongue
- English
- Weight
- 127 KB
- Volume
- 252
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
In a previous paper the author has generalized the Kähler angle to the multiple Kähler angle and formulated a Poincaré formula for any real submanifolds in complex projective spaces ℂ__P__^n^ using the multiple Kähler angles of the submanifolds. In this paper we formulate a Poincaré formula for submanifolds M and N of complementary dimension in ℂ__P__^n^ by a symmetric polynomial of degree one in cos^2^ θ~i~ and cos^2^ τ~j~, where θ~i~ and τ~j~ are the multiple Kähler angles of M and N. We also obtain some inequalities between the integral of the intersection numbers of submanifolds and their volumes in some cases.