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Generalization of Kähler angle and integral geometry in complex projective spaces II
Author(s) -
Tasaki Hiroyuki
Publication year - 2003
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310040
Subject(s) - mathematics , generalization , complex projective space , projective space , pure mathematics , projective test , collineation , geometry , mathematical analysis
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.