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Đường Lagrangian trong Không gian Liên hợp Phi tuyến bốn Chiều
Tóm tắt
Các đường Lagrangian trong \(\mathbb {R}^{4}\) có những mối quan hệ thú vị với biến dạng bậc hai của các đường phẳng dưới nhóm affine đặc biệt và các đường null trong một dạng không gian Lorentz ba chiều. Chúng tôi cung cấp một khung liên hợp phi tuyến tự nhiên cho các đường Lagrangian. Điều này cho phép chúng tôi phân loại các đường Lagrangian có độ cong symplectic không đổi, xây dựng một lớp các torus Lagrangian trong \(\mathbb {R}^{4}\) và xác định các đường geodesic Lagrangian.
Từ khóa
#Đường Lagrangian #không gian symplectic #biến dạng bậc hai #đường geodesic #không gian Lorentz #lớp torus Lagrangian.Tài liệu tham khảo
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