Stable Forms, Vector Cross Products and Their Applications in Geometry

Abstract

The connection between Hitchin's stable forms and vector cross products is observed. Using this correspondence, we construct new examples of non-Kahler Calabi-Yau 3-folds and manifolds with G2-structure of class W3. We also generalize and refine results of Calabi and Gray in the paracomplex setting.

23 pages, comments are welcome! Updates in v2: more references are added, discussion on Killing spinor equation is included

References in corpus (8)

• Geometric Model for Complex Non-Kaehler Manifolds with SU(3) Structure
• Killing spinor equations in dimension 7 and geometry of integrable G_2-manifolds
• The geometry of a bi-Lagrangian manifold
• Invariant Solutions to the Strominger System on Complex Lie Groups and Their Quotients
• Duality and Fibrations on G_2 Manifolds
• Non-Kaehler SYZ mirror symmetry
• Homogeneous para-Kähler Einstein manifolds
• Ricci Curvatures on Hermitian manifolds

Cited by in corpus (7)

• A Construction of Non-Kähler Calabi-Yau Manifolds and New Solutions to the Strominger System
• New curvature flows in complex geometry
• A flow of conformally balanced metrics with Kähler fixed points
• Coclosed $G_2$-structures inducing nilsolitons
• $T^4$ fibrations over Calabi-Yau two-folds and non-Kahler manifolds in string theory
• Invariant cocalibrated $G_2$-structures on nilmanifolds
• Convergence of Hermitian manifolds and the Type IIB flow