JOSAI MATHEMATICAL MONOGRAPHS

JMM 3. Differential Geometry

Proceedings of the First International Symposium on Differential Geometry

held at Josai University, February 22 -- 24, 2001

JOSAI UNIVERSITY

Edited by

Qing-Ming CHENG

Department of Mathematics

Josai University

Contents

Foreword …………………………………………………… v

Preface …………………………………………………… vi

Program …………………………………………………… vii

List of the Contributors ………………………………ix

Construction of flat tori in the 3-sphere and its applications

By Yoshihisa Kitagawa …………………………………….3

Some Liouville type inequalities and its applications to geometric problems

By Young Jin Suh …………………………………………11

On diffeomorphisms of a hyperbolic manifold

By Midori Goto ………………………………………………21

Schrodinger flow and its applications in integrable systems

By Qing Ding ………………………………………………23

On surfaces with holomorphic Gauss map in a certain symmetric space

By Masatoshi Kokubu …………………………………… 37

On the Goldberg conjecture

By Kouei Sekigawa …………………………………………43

Acute triangulations of sphere and icosahedron

By Jinichi Itoh ………………………………………………53

Some geometric properties of p-harmonic maps

By Shigeo Kawai ……………………………………………63

Maximum principles and its applications to submanifolds

By Katsuhiro Nonaka ………………………………………71

Comparison theorems for Riemannian manifolds with radial curvature

By Katsuhiro Shiohama ……………………………………81

On Anand conjecture

By YuXin Dong ………………………………………………93

Notes on the relative Yamabe invariant

By Kazuo Akutagawa ………………………………………105

Complete submanifolds in spheres

By Qing-Ming Cheng ………………………………………115

Submanifolds with degenerate Gauss mapping

By Goo Ishikawa, Makoto Kimura and Reiko Miyaoka …125

Total curvature for open submanifolds of Euclidean spaces

By Franki Dillen and Wolfgang Kuhnel …………………………139

Existence of a family of complete minimal surfaces of genus one with one end and finite

total curvature

By Katsuhiro Moriya …………………………………………149

Programme of the Symposium

Differential Geometry

The First International Symposium on Differential Geometry

February 22-24, 2001, Josai University, Sakado, Saitama, Japan

Programme

February 22

13.10 -- 13.55

Yoshihisa Kitagawa (Utsunomiya University)

Construction of flat tori in the 3-sphere and its applications

14.05 -- 14.50

Young Jin Suh (Kyungpook National University)

Some Liouville type inequalities and its applications to geometric problems

15.10 -- 15.30

Midori Goto (Fukuoka Institute of Technology)

On diffeomorphisms of a hyperbolic manifold

15.40 -- 16.25

Qing Ding (Fudan Unversity)

Schrodinger flow and its applications in integrable systems

16.35 -- 17.20

Masatoshi Kokubu (Denki University of Tokyo)

On surfaces with holomorphic Gauss map in a certain symmetric space

February 23

9.00 -- 9.45

Kouei Sekigawa (Niigata University)

On the Goldberg conjecture

9.55 -- 10.40

Jinichi Itoh (Kumamoto University)

Acute triangulations of sphere and icosahedron

11.00 -- 11.45

Shigeo Kawai (Saga University)

Some geometric properties of p-harmonic maps

11.55 -- 12.15

Katsuhiro Nonaka (Josai University)

Maximum principles and its applications to submanifolds

13.40 -- 14.25

Katsuhiro Shiohama (Saga University)

Comparison theorems for Riemannian manifolds with radial curvature

bounded below

14.35 -- 15.20

YuXin DONG (Fudan University)

On Anand conjecture

15.40 -- 4.25

Kazuo Akutagawa (Shizuoka University)

Notes on the relative Yamabe invariant

16.35 -- 17.20

Qing-Ming Cheng (Josai University)

Complete submanifolds in spheres

February 24

9.00 -- 9.45

Goo Ishikawa, Makoto Kimura and Reiko Miyaoka (Sophia University)

Submanifolds with degenerate Gauss mapping

9.55 -- 10.40

Franki Dillen and Wolfgang Kuhnel (Katholieke University Leuven)

Total curvature for open submanifolds of Euclidean spaces

11.00 -- 11.45

Katsuhiro Moriya (University of Tsukuba)

Existence of a family of complete minimal surfaces of genus one with one

end and finite total curvature