Completeness in affine and statistical geometry

被引:4
作者
Opozda, Barbara [1 ]
机构
[1] Fac Math & Comp Sci UJ, Ul Lojasiewicza 6, PL-30348 Krakow, Poland
关键词
Affine connection; Geodesic; Completeness; Affine hypersurface; Statistical structure; HYPERSURFACES;
D O I
10.1007/s10455-021-09752-x
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We begin the study of completeness of affine connections, especially those on statistical manifolds or on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.
引用
收藏
页码:367 / 383
页数:17
相关论文
共 12 条
[1]  
[Anonymous], 1993, Global Affine Differential Geometry of Hypersurfaces
[2]  
Calabi E, 1972, Ist. NAZ Alta Mat. Sym. Mat., P19
[3]   COMPLETE AFFINE HYPERSURFACES .1. THE COMPLETENESS OF AFFINE METRICS [J].
CHENG, SY ;
YAU, ST .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1986, 39 (06) :839-866
[4]   CONJUGATE CONNECTIONS AND RADON THEOREM IN AFFINE DIFFERENTIAL GEOMETRY [J].
DILLEN, F ;
NOMIZU, K ;
VRANKEN, L .
MONATSHEFTE FUR MATHEMATIK, 1990, 109 (03) :221-235
[5]  
Hu ZJ, 2011, J DIFFER GEOM, V87, P239, DOI 10.4310/jdg/1304514974
[6]  
Kobayashi Shoshichi, 1963, Foundations of differential geometry, V1
[7]  
Noguchi M., 1992, Differential Geometry and its Applications, V2, P197, DOI DOI 10.1016/0926-2245(92)90011-B
[8]  
NOMIZU K, 1986, GEOMETRIAE DEDICATA, V20, P43
[9]  
Nomizu K., 1994, Cambridge Tracts in Mathematics
[10]   Bochner's technique for statistical structures [J].
Opozda, Barbara .
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2015, 48 (04) :357-395