We describe two constructions of hyperkahler manifolds, one based on a Legendre transform, and one on a sympletic quotient. These constructions arose in the context of supersymmetric nonlinear σ-models, but can be described entirely geometrically. In this general setting, we attempt to clarify the relation between supersymmetry and aspects of modern differential geometry, along the way reviewing many basic and well known ideas in the hope of making them accessible to a new audience.

/pdf/hyperkahler-metrics-and-supersymmetry-4al39d7k9z.pdf

Hyperkahler Metrics and Supersymmetry

Nonlinear models in 2 + ε dimensions☆

/pdf/pseudo-hermitian-structures-on-a-real-hypersurface-4rb9axvry0.pdf

Pseudo-Hermitian structures on a real hypersurface

We analyze the necessary and sufficient conditions for the preservation of supersymmetry for bosonic geometries of the form ${R}^{1,9\ensuremath{-}d}\ifmmode\times\else\texttimes\fi{}{M}_{d},$ in the common Neveu-Schwarz--Neveu-Schwarz (NS-NS) sector of type II string theory and also type I or heterotic string theory. The results are phrased in terms of the intrinsic torsion of G structures and provide a comprehensive classification of static supersymmetric backgrounds in these theories. Generalized calibrations naturally appear since the geometries can always arise as solutions describing NS or type I or heterotic fivebranes wrapping calibrated cycles. Some new solutions are presented. In particular we find $d=6$ examples with a fibered structure which preserve $\mathcal{N}=1,2,3$ supersymmetry in type II and include compact type I or heterotic geometries.

Superstrings with intrinsic torsion

https://pure.rug.nl/ws/files/14495060/1988AnnPhysBergshoeff.pdf

Properties of the eleven-dimensional supermembrane theory

Structures on manifolds

*Frontmatter, pg. i*Preface, pg. v*Contents, pg. vii*Chapter I. Riemannian Manifold, pg. 2*Chapter II. Harmonic and Killing Vectors, pg. 26*Chapter III. Harmonic and Killing Tensors, pg. 59*Chapter IV. Harmonic and Killing Tensors in Flat Manifolds, pg. 77*Chapter V. Deviation from Flatness, pg. 81*Chapter VI. Semi-simple Group Spaces, pg. 90*Chapter VII. Pseudo-harmonic Tensors and Pseudo-Killing Tensors in Metric Manifolds with Torsion, pg. 97*Chapter VIII. Kaehler Manifold, pg. 117*Chapter IX. Supplements, pg. 170*Bibliography, pg. 187*Backmatter, pg. 192

健太郎矢野

Papers

Structures on manifolds

Curvature and Betti numbers

Integral formulas in Riemannian geometry

Tangent and cotangent bundles : differential geometry

The theory of Lie derivatives and its applications

健太郎 矢野

Papers

Structures on manifolds

Curvature and Betti numbers

Integral formulas in Riemannian geometry

Tangent and cotangent bundles : differential geometry

The theory of Lie derivatives and its applications

健太郎矢野