Symmetric spaces as adjoint orbits and their geometries

Author(s)

Cavenaghi, Leonardo F. ; Garcia, Carolina ; Grama, Lino ; Martin, Luiz A. B. San

• Document type: Journal article
• Source: REVISTA MATEMATICA COMPLUTENSE; v. 37, n. 3, p. 46-pg., 2024-03-21.

Abstract

We realize specific classical symmetric spaces, like the semi-Kahler symmetric spaces discovered by Berger, as cotangent bundles of symmetric flag manifolds. These realizations enable us to describe these cotangent bundles' geodesics and Lagrangian submanifolds. As a final application, we present the first examples of vector bundles over simply connected manifolds with nonnegative curvature that cannot accommodate metrics with nonnegative sectional curvature, even though their associated unit sphere bundles can indeed accommodate such metrics. Our examples are derived from explicit bundle constructions over symmetric flag spaces. (AU)

• FAPESP's process: 22/09603-9 - Positive curvatures, exotic manifolds and Riemannian foliations
• Grantee: Leonardo Francisco Cavenaghi
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 21/04065-6 - BRIDGES: Brazil-France interplays in Gauge Theory, extremal structures and stability
• Grantee: Henrique Nogueira de Sá Earp
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 18/13481-0 - Geometry of control, dynamical and stochastic systems
• Grantee: Marco Antônio Teixeira
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 23/13131-8 - Invariant Hermitian structures and geometric flows on homogeneous spaces
• Grantee: Lino Anderson da Silva Grama
• Support Opportunities: Regular Research Grants
• FAPESP's process: 23/14316-1 - Spherical T-duality and exotic spheres
• Grantee: Leonardo Francisco Cavenaghi
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor