tt∗-geometry on the tangent bundle of an almost complex manifold
tt∗-geometry on the tangent bundle of an almost complex manifold
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几乎复流形的切束上的 tt*-几何
DOI：
10.1016/j.geomphys.2006.08.004
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发表时间：
2007
影响因子：
1.5
通讯作者：
L. Schäfer
中科院分区：
文献类型：
--
作者：
L. Schäfer
本文研究几乎复流形（M，J）上的t-丛（TM，D，S）.设M是M上的平坦联络。刻画了由单参数联络族<$θ=exp（θJ）<$$><$exp（−θ J）诱导的满足<$=D+S的tt-丛，得到了D为复的解的唯一性结果.这类解的一个子类是平坦的近Kähler流形和特殊Kähler流形。此外，我们还研究了这些tt-丛具有辛或度量tt-丛结构的情形。最后，我们将多调和映射的概念推广到几乎复流形（M，J）到伪黎曼流形的映射，并将上述辛和度量tt-丛分别与从（M，J）到伪黎曼对称空间SO_0（p，q）/U（p，q）和Sp（R ~ 2n）/U（p，q）的多调和映射联系起来.
The subject of this paper is tt∗-bundles (TM,D,S) over an almost complex manifold (M,J). Let ∇ be a flat connection on M. We characterize those tt∗-bundles with ∇=D+S which are induced by the one parameter family of connections ∇θ=exp(θJ)∘∇∘exp(−θJ) and obtain a uniqueness result for solutions where D is complex. A subclass of such solutions is flat nearly Kähler manifolds and special Kähler manifolds. Moreover, we study the case where these tt∗-bundles admit the structure of symplectic or metric tt∗-bundles. Finally, we generalize the notion of pluriharmonic maps to maps from almost complex manifolds (M,J) into pseudo-Riemannian manifolds and relate the above symplectic and metric tt∗-bundles to pluriharmonic maps from (M,J) into the pseudo-Riemannian symmetric spaces SO0(p,q)/U(p,q) and Sp(R2n)/U(p,q), respectively.