Riemannian submanifolds and geometry of Laplace operator

Research Project

Project/Area Number	24540073
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Multi-year Fund
Section	一般
Research Field	Geometry
Research Institution	Shizuoka University
Principal Investigator	Kumura Hironori 静岡大学, 理学部, 准教授 (30283336)
Project Period (FY)	2012-04-01 – 2016-03-31
Project Status	Completed (Fiscal Year 2015)
Budget Amount *help	¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000) Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000) Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000) Fiscal Year 2012: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Keywords	部分多様体 / ラプラス作用素 / 平均曲率 / submersion / ラプラス-ベルトラミ作用素 / 固有値 / ラプラシアン / 等長的はめ込み
Outline of Final Research Achievements	Riemannian submanifolds M may exit from a domain of target manifold, if the norm of the curvature of M and the second fundamental form are sufficiently small compared to the target manifolds. In this respect, I considered the case the target manifolds are Riemannian submersion and extended the results of previous paper. I calculate exit radii from cylinderorical domain using the geometric quantity explicitly. I also consider the relationship possibility of immersion and the eigenvalue of the Laplacian.