Compact lcK manifolds with parallel vector fields

• Autorzy: Andrei Moroianu
• Języki publikacji: EN

Abstrakty

EN

We show that for n > 2 a compact locally conformally Kähler manifold (M2n , g, J) carrying a nontrivial parallel vector field is either Vaisman, or globally conformally Kähler, determined in an explicit way by a compact Kähler manifold of dimension 2n − 2 and a real function.

Słowa kluczowe

EN

Vaisman manifolds; lcK manifolds; parallel vector fields

• Wydawca: De Gruyter Open
• Czasopismo: Complex Manifolds
• Rocznik: 2015
• Tom: 2
• Numer: 1

Daty

otrzymano

2015-05-13

zaakceptowano

2015-05-30

online

2015-07-09

Twórcy

autor

Andrei Moroianu

• Université de Versailles-St Quentin, Laboratoire de Mathématiques, UMR 8100 du
  CNRS, 45 avenue des États-Unis, 78035 Versailles, France

Bibliografia

• [1] F. Belgun, On the metric structure of non-Kähler complex surfaces, Math. Ann. 317 (2000), 1–40.
• [2] N. Buchdahl, On compact Kähler surfaces, Ann. Inst. Fourier 49 no. 1 (1999), 287–302. [Crossref]
• [3] S. Dragomir, L. Ornea, Locally conformal Kähler geometry, Progress in Math. 155, Birkhäuser, Boston, Basel, 1998.
• [4] P. Gauduchon, A. Moroianu, L. Ornea, Compact homogeneous lcK manifolds are Vaisman, Math. Ann. 361 (3-4), (2015), 1043– 1048. [WoS]
• [5] P. Gauduchon, L. Ornea, Locally conformally Kähler metrics on Hopf surfaces, Ann. Inst. Fourier 48 no. 4 (1998), 1107–1127. [Crossref]
• [6] A. Lamari, Courants kählériens et surfaces compactes, Ann. Inst. Fourier 49 no. 1 (1999), 263–285. [Crossref]
• [7] L. Ornea, M. Verbitsky, Structure theorem for compact Vaisman manifolds, Math. Res. Lett., 10 (2003), 799–805.
• [8] I. Vaisman, A survey of generalizedHopf manifolds, Rend. Sem.Mat. Univ. Politec. Torino 1983, Special Issue (1984), 205–221.

Identyfikatory

DOI

10.1515/coma-2015-0004