Stable submanifolds in the product of projective spaces II Stable submanifolds in the product of projective spaces II

• Published in: Calculus of variations and partial differential equations Vol. 64; no. 5
• Main Authors: Chen, Shuli, Ramirez-Luna, Alejandra
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2025; Springer Nature B.V
• Subjects: Analysis; Calculus of Variations and Optimal Control; Optimization; Control; Manifolds (mathematics); Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Riemann manifold; Subspaces; Systems Theory; Theoretical; 53C42; 53C40
• ISSN: 0944-2669; 1432-0835
• DOI: 10.1007/s00526-025-03006-5

We prove that there do not exist odd-dimensional stable compact minimal immersions in the product of two complex projective spaces. We also prove that the only stable compact minimal immersions in the product of a quaternionic projective space with any other Riemannian manifold are the products of quaternionic projective subspaces with compact stable minimal immersions of the second manifold in the Riemannian product. These generalize similar results of the second-named author of immersions with low dimensions or codimensions to immersions with arbitrary dimensions. In addition, we prove that the only stable compact minimal immersions in the product of an octonionic projective plane with any other Riemannian manifold are the products of octonionic projective subspaces with compact stable minimal immersions of the second manifold in the Riemannian product.