Nonexistence of stable currents in submanifolds of a product of two spheres

DOI10.1017/S0004972700029762zbMath0725.49016MaRDI QIDQ5201838

Xue-Shan Zhang

Publication date: 1991

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

homology groupimmersed submanifoldsselfadjoint linear operatornonexistence of stable integral currentsstable p-current

Mathematics Subject Classification ID

Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Global submanifolds (53C40) Variational problems concerning extremal problems in several variables; Yang-Mills functionals (58E15) Singular homology and cohomology theory (55N10)

Related Items (10)

Geometry and topology of submanifolds immersed in space forms and ellipsoids ⋮ Nonexistence of stable currents ⋮ On the topology of CR-warped product submanifolds ⋮ Null homology in warped product Lagrangian submanifolds of the nearly Kaehler \(\mathbb{S}^6\) and its applications ⋮ VANISHING AND TOPOLOGICAL SPHERE THEOREMS FOR SUBMANIFOLDS IN A HYPERBOLIC SPACE ⋮ On the nonexistence of stable currents in submanifolds of a Euclidean space ⋮ Homology groups in warped product submanifolds in hyperbolic spaces ⋮ Stable currents and homology groups in a compact CR-warped product submanifold with negative constant sectional curvature ⋮ On the limit cycles of quadratic differential systems. ⋮ Homology of submanifolds of six dimensional sphere

Cites Work

• On stable currents and their application to global problems in real and complex geometry
• Normal and integral currents

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