A NON-EXISTENCE THEOREM FOR MORSE TYPE HOLOMORPHIC FOLIATIONS OF CODIMENSION ONE TRANSVERSE TO SPHERES

被引：4

作者：

Ito, Toshikazu ^{[1
]}

Scardua, Bruno

机构：

[1] Ryukoku Univ, Dept Nat Sci, Fushimi Ku, Kyoto 612, Japan

来源：

INTERNATIONAL JOURNAL OF MATHEMATICS | 2010年 / 21卷 / 04期

关键词：

Holomorphic foliation; Morse type singularity; transversality; Poincare-Hopf index;

D O I：

10.1142/S0129167X1000615X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that a Morse type codimension one holomorphic foliation is not transverse to a sphere in the complex affine space. Also we characterize the variety of contacts of a linear foliation with concentric spheres.

引用

页码：435 / 452

页数：18

共 11 条

[1]

[Anonymous], RIMS KOKYUROKU

[2]

ARNOLD VI, 1969, FUNCTIONAL ANAL APPL, V3, P1

[3]

Camacho C., 1978, PUBLICATIONS MATH, V48, P5, DOI 10.1007/BF02684312

[4]

Camacho C., 1985, GEOMETRIC THEORY FOL

[5] TOPOLOGY OF A HOLOMORPHIC VECTOR FIELD AROUND AN ISOLATED SINGULARITY [J].

GOMEZMONT, X ;

SEADE, J ;

VERJOVSKY, A .

FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 1993, 27 (02) :97-103

[6]

GUCKENHEIMER J, 1972, COMPOS MATH, V24, P75

[7]

Ito T, 2005, MATH RES LETT, V12, P713

[8] A Poincare-Hopf-type theorem for holomorphic one-forms [J].

Ito, T ;

Scárdua, B .

TOPOLOGY, 2005, 44 (01) :73-84

[9] ON HOLOMORPHIC FOLIATIONS TRANSVERSE TO SPHERES [J].

Ito, Toshikazu ;

Scardua, Bruno .

MOSCOW MATHEMATICAL JOURNAL, 2005, 5 (02) :379-397

[10]

MALGRANGE B, 1976, PUBL MATH-PARIS, V46, P162

← 1 2 →