A classification of surfaces with isotropic Para‐Blaschke tensor. Issue 9 (15th June 2020)

• Record Type: Journal Article
• Authors: Li, Fengjiang; Fang, Jianbo; Li, Jianxiang
• Is Part Of: Mathematische Nachrichten. Volume 293:Issue 9(2020)
• Page Start: 1762
• Page End: 1775
• Publication Date: 2020-06-15
• Subjects: closed Möbius form -- isotropic -- Möbius geometry -- Para‐Blaschke tensor -- 53A30 -- 53B25; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201900222
• Languages: English
• ISSNs: 0025-584X

Abstract

Abstract: Let M 2 → S 3 be an umbilic‐free surface. Four basic invariants of M 2 under the Möbius transformation group of S 3 are the Möbius metric g, the Blaschke tensor A, the Möbius second fundamental form B and the Möbius form Φ. A symmetric (0, 2) tensor D = A + μ B called Para‐Blaschke tensor, where μ is constant, is also Möbius invariant. In this paper, we classify the surfaces with isotropic Para‐Blaschke tensor ( D = λ g, where λ is a function).