NAGATOMO Yasuyuki    Department   Undergraduate School  , School of Science and Technology    Position   Professor
Research Period	2000～2001
Research Topic	Homogeneous spaces and variational problems
Research Type	KAKENHI Research
Consignor	Japan Society for the Promotion of Science
Research Program Type	Grant-in-Aid for Scientific Research (C)
KAKENHI Grant No.	12640058
Keyword	Kahler angle, variational problem, integral geometry, symmetric space, homogeneous space
Responsibility	Research Contributor
Representative Person	TASAKI Hiroyuki
Details	The head investigator has developed explicit expressions of Poincare integral formulas in order to apply these formulas of integral geometry to variational problems in homogeneous spaces. He has obtained an explicit representa tion of Poincare formula of real surfaces in the complex projective spaces in terms of the Kahler angles of those surfaces. This is the first explicit one in which the integral of intersection numbers is not expressed by the product of the volumes of submanifolds. After this in order to generalize this formula to those for general real submanifolds in the complex projective spaces he defined multiple Kahler angles which were generalizations of Kahler angle. According to the multiple Kahler angle he has developed Poincare formulas of general real submanifolds in the complex projective spaces. As a conse quence a relation among some integrals of the multiple Kahler angles and the volumes of submanifolds can be obtained and will become a tool for variational problems.