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SYZ mirror symmetry of solvmanifolds
Full text linkWe present an effective construction of non-Kaehler supersymmetric mirror pairs in the sense of Lau,Tseng and Yau starting from left-invariant affine structures on Lie groups. Applying this construction we explicitly find SYZ mirror symmetric partners of all known compact 6-dimensional completely solvable solvmanifolds that admit a semi-flat type IIA structure.28 pages, 2 tables. References to related results have been added. Comments are welcom
Remarks on Kaehler-Ricci solitons
No full textWe prove that a complex compact manifold endowed with a Kehler Ricci soliton cannot be isometrically embedded in a complex projective space CPn in such a way that the Gauss map is rational, unless the metric is Einstein. This applies to hypersurfaces of complex compact homogeneous spaces canonically embedded in CPn.
We moreover obtain two curvature constraints for invariant Kaehler Ricci solitons on complex manifolds acted on by a compact Lie group with cohomogeneity one
A Hamiltonian stable minimal Lagrangian submanifold of projective space with non-parallel second fundamental form
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