Connexions with Totally Skew-symmetric Torsion and Nearly-kähler Geometry
نویسنده
چکیده
We study almost Hermitian structures admitting a Hermitian connexion with totally skew-symmetric torsion or equivalently, those almost Hermitian structures with totally skewsymmetric Nijenhuis tensor. We investigate up to what extent the Nijenhuis tensor fails to be parallel with respect to the characteristic connexion. This is naturally described by means of an extension of the notion of Killing form to almost Hermitian geometry. In this context, we also make an essentially self-contained survey of nearly-Kähler geometry, but from the perspective of non-integrable holonomy systems.
منابع مشابه
Geometry of Quaternionic Kähler connections with torsion
The target space of a (4,0) supersymmetric two-dimensional sigma model with Wess-Zumino term has a connection with totally skew-symmetric torsion and holonomy contained in Sp(n).Sp(1), QKT-connection. We study the geometry of QKT-connections. We find conditions to the existence of a QKT-connection and prove that if it exists it is unique. Studying conformal transformations we obtain a lot of (c...
متن کاملQuaternionic Kähler and hyperKähler manifolds with torsion and twistor spaces
The target space of a (4,0) supersymmetric two-dimensional sigma model with Wess-Zumino term has a connection with totally skew-symmetric torsion and holonomy contained in Sp(n)Sp(1) (resp. Sp(n)), QKT (resp. HKT)-spaces. We study the geometry of QKT, HKT manifold and their twistor spaces. We show that the Swann bundle of a QKT manifold admits a HKT structure with special symmetry if and only i...
متن کاملOn Types of Non-integrable Geometries
We study the types of non-integrable G-structures on Riemannian manifolds. In particular, geometric types admitting a connection with totally skew-symmetric torsion are characterized. 8-dimensional manifolds equipped with a Spin(7)-structure play a special role. Any geometry of that type admits a unique connection with totally skew-symmetric torsion. Under weak conditions on the structure group...
متن کاملSpin(9)-structures and Connections with Totally Skew-symmetric Torsion
We study Spin(9)-structures on 16-dimensional Riemannian manifolds and characterize the geometric types admitting a connection with totally skew-symmetric torsion.
متن کاملAn intrinsic volume functional on almost complex 6-manifolds and nearly Kähler geometry
Let (M, I) be an almost complex 6-manifold. The obstruction to integrability of almost complex structure (socalled Nijenhuis tensor) N : Λ0,1(M)−→ Λ(M) maps a 3-dimensional bundle to a 3-dimensional one. We say that Nijenhuis tensor is non-degenerate if it is an isomorphism. An almost complex manifold (M, I) is called nearly Kähler if it admits a Hermitian form ω such that ∇(ω) is totally antis...
متن کامل