- and -manifolds" target="_blank">Frölicher-Nijenhuis cohomology on - and -manifolds
Kotaro Kawai   Hông Vân Lê   Lorenz Schwachhöfer   
2017年3月
In this paper we show that a parallel differential form of even degree<br />
on a Riemannian manifold allows to define a natural differential both on<br />
and , defined via the<br />
Fr\"olicher-Ni...
-manifolds" target="_blank">Second order deformations of associative submanifolds in nearly parallel -manifolds
Kotaro Kawai   
2016年10月
Associative submanifolds in nearly parallel -manifolds are<br />
minimal 3-submanifolds in spin 7-manifolds with a real Killing spinor. The<br />
Riemannian cone over has the holonomy group contained in <br />
and t...
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS 47 159-189 2016年8月
We introduce the notion of affine Legendrian submanifolds in Sasakian manifolds and define a canonical volume called the phi-volume as odd dimensional analogues of affine Lagrangian (totally real or purely real) geometry. Then we derive the second...
-and -manifolds" target="_blank">Frölicher-Nijenhuis bracket and geometry of -and -manifolds
Kotaro Kawai   Hông Vân Lê   Lorenz Schwachhöfer   
2016年5月
We extend the characterization of the integrability of an almost complex<br />
structure on differentiable manifolds via the vanishing of the<br />
Fr\"olicher-Nijenhuis bracket to an analogous characterization<br />
of tor...
QUARTERLY JOURNAL OF MATHEMATICS 66(3) 861-893 2015年9月
The squashed 7-sphere S-7 is a 7-sphere with an Einstein metric given by the canonical variation and its cone R-8 - {0} has full holonomy Spin(7). There is a canonical calibrating 4-form Phi on R-8 - {0}. A minimal 3-submanifold in S-7 is called a...