GEODESICS IN THE SPACE OF KAHLER METRICS

被引：32

作者：

Lempert, Laszlo ^{[1
]}

Vivas, Liz ^{[1
]}

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

来源：

DUKE MATHEMATICAL JOURNAL | 2013年 / 162卷 / 07期

基金：

美国国家科学基金会;

关键词：

COMPLEX MONGE-AMPERE; MANIFOLDS; EQUATION; DOMAINS;

D O I：

10.1215/00127094-2142865

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (X, omega) be a compact Kahler manifold. As discovered in the late 1980s by Mabuchi, the set H-0 of Kahler forms cohomologous to omega has the natural structure of an infinite-dimensional Riemannian manifold. We address the question of whether any two points in H-0 can be connected by a smooth geodesic and show that the answer, in general, is "no."

引用

页码：1369 / 1381

页数：13

共 14 条

[1]

[Anonymous], 2012, Adv. Lect. Math

[2]

[Anonymous], 1933, Fundamenta Mathematicae

[3] FOLIATIONS AND COMPLEX MONGE-AMPERE EQUATIONS [J].

BEDFORD, E ;

KALKA, M .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1977, 30 (05) :543-571

[4] STABILITY OF ENVELOPES OF HOLOMORPHY AND THE DEGENERATE MONGE-AMPERE EQUATION [J].

BEDFORD, E .

MATHEMATISCHE ANNALEN, 1982, 259 (01) :1-28

[5] EXTREMAL PLURISUBHARMONIC FUNCTIONS FOR CERTAIN DOMAINS IN C2 [J].

BEDFORD, E .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1979, 28 (04) :613-626

[6]

BEDFORD E., INVENT MATH, V50, P129, DOI [10.1007/BF01390286, DOI 10.1007/BF01390286.(1370)]

[7]

BOCHNER S., 1948, PRINCETON MATH SER

[8]

Chen XX, 2000, J DIFFER GEOM, V56, P189

[9]

Donaldson S.K., 1999, American Mathematical Society Translations-Series, V196, P13

[10]

Donaldson SK., 2002, J. Symplectic Geom., V1, P171, DOI 10.4310/JSG.2001.v1.n2.a1

← 1 2 →