The (𝑀₊,𝑀₋)-method on compact symmetric spaces and its applications

DOI10.1090/conm/777/15624zbMath1501.53071OpenAlexW4226490107MaRDI QIDQ5085350

Bang-Yen Chen

Publication date: 27 June 2022

Published in: Differential Geometry and Global Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/conm/777/15624

zbMATH Keywords

polarcompact symmetric spaceantipodalmeridian

Mathematics Subject Classification ID

Global submanifolds (53C40) Differential geometry of symmetric spaces (53C35) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Cites Work

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• The 2-ranks of connected compact Lie groups
• Lagrangian Floer homology of a pair of real forms in Hermitian symmetric spaces of compact type
• Homotopy of EVII
• The intersection of two real forms in the complex hyperquadric
• The geometry of symmetric triad and orbit spaces of Hermann actions
• Two-numbers and their applications -- a survey
• Spheres in Hermitian symmetric spaces and flag manifolds
• The projective rank of a Hermitian symmetric space: A geometric approach and consequences
• Periodic maps in symplectic topology
• Stability of certain minimal submanifolds of compact Hermitian symmetric spaces
• Harmonic metrics, harmonic tensors, and Gauss maps
• Stability of closed Lie subgroups in compact Lie groups
• `Spindles' in symmetric spaces
• Spinor groups and algebraic coding theory
• Stability of certain minimal submanifolds in compact symmetric spaces of rank two
• Totally geodesic submanifolds in compact symmetric spaces of rank two
• Stable minimal submanifolds in compact rank one symmetric spaces
• 2-tori in \(E_ 8\)
• The involutions of the compact symmetric spaces
• Morse theory for Lagrangian intersections
• Convexity properties of the moment mapping
• The spheres in symmetric spaces
• The involutions of compact symmetric spaces. II
• On the stability of Cartan embeddings of compact symmetric spaces
• Stability of \(p\)-harmonic maps
• On the 2-rank of compact connected Lie groups
• Totally geodesic submanifolds of symmetric spaces. I
• Totally geodesic submanifolds of symmetric spaces. II
• The involutions of compact symmetric spaces. IV
• Totally geodesic submanifolds in compact Riemannian symmetric spaces and their stability
• Polar sets as nondegenerate critical submanifolds in symmetric spaces
• Tight Lagrangian submanifolds in \({\mathbb{C}}P^ n\)
• Arithmetic distance on compact symmetric spaces
• On stable currents and their application to global problems in real and complex geometry
• The involutions of compact symmetric spaces. III
• Stability of minimal submanifolds in symmetric spaces
• The intersection of two real forms in Hermitian symmetric spaces of compact type
• Convexity of reflective submanifolds in symmetric \(R\)-spaces
• Bott periodicity for inclusions of symmetric spaces
• Antipodal sets of symmetric \(R\)-spaces
• Antipodal sets and designs on unitary groups
• Great antipodal sets on complex Grassmannian manifolds as designs with the smallest cardinalities
• The intersection of two real forms in Hermitian symmetric spaces of compact type. II.
• Maximal tori of extrinsic symmetric spaces and meridians
• Projective ranks of Hermitian symmetric spaces
• The stable homotopy of the classical groups
• Totally geodesic spheres in compact symmetric spaces
• Clifford modules
• The index of elliptic operators. III
• Minimal varieties in Riemannian manifolds
• The periodicity theorem for the classical groups and some of its applications
• The spectrum of an equivariant cohomology ring. I. II
• Elliptic spaces in Grassmann manifolds
• On the geometry of algebraic homogeneous spaces
• Sur certaines sous-groupes des groupes de Lie compacts
• Centrioles in symmetric spaces
• ANTIPODAL SETS IN ORIENTED REAL GRASSMANN MANIFOLDS
• The Invariant of Chen-Nagano on Flag Manifolds
• ANTIPODAL SETS OF COMPACT SYMMETRIC SPACES AND THE INTERSECTION OF TOTALLY GEODESIC SUBMANIFOLDS
• A Riemannian Geometric Invariant and its Applications to a Problem of Borel and Serre
• Two-number of symmetric R-spaces
• Convexity and Commuting Hamiltonians
• Homotopy of compact symmetric spaces
• The index number of an 𝑅-space: An extension of a result of M.Takeuchi’s
• Maximal Antipodal Subgroups of the Automorphism Groups of Compact Lie Algebras
• Conjugate Loci of Totally Geodesic Submanifolds of Symmetric Spaces
• Convexity and Tightness for Restrictions of Hamiltonian Functions to Fixed Point Sets of an Antisymplectic Involution
• Geometry of Symmetric R-spaces
• The fixed point set of a holomorphic isometry, the intersection of two real forms in a Hermitian symmetric space of compact type and symmetric triads
• Estimates of antipodal sets in oriented real Grassmann manifolds
• Transformation Groups on Compact Symmetric Spaces
• Generalized symmetric spaces
• The involutions of compact symmetric spaces. V
• On index number and topology of flag manifolds