Phương trình Kazdan-Warner tổng quát liên quan đến hành động tuyến tính của vành tròn trên không gian vector phức

Geometriae Dedicata - Tập 214 - Trang 651-669 - 2021
Natsuo Miyatake1
1Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, Japan

Tóm tắt

Chúng tôi giới thiệu các phương trình Kazdan-Warner tổng quát trên các đa tạp Riemann liên quan đến một hành động tuyến tính của một vành tròn trên không gian vector phức. Chúng tôi chứng minh sự tồn tại và tính duy nhất của nghiệm cho phương trình trên bất kỳ đa tạp Riemann compact nào. Như một ứng dụng, chúng tôi đưa ra một bằng chứng mới cho một định lý của Baraglia [5], theo đó một bó Higgs chu kỳ cung cấp một nghiệm cho phương trình Toda tuần hoàn.

Từ khóa

#Kazdan-Warner #đa tạp Riemann #bó Higgs #phương trình Toda tuần hoàn

Tài liệu tham khảo

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