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Totally geodesic and parallel hypersurfaces of 4-dimensional Lorentzian nilpotent Lie groups
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This paper investigates the four-dimensional 2-step nilpotent Lie group $H_{3}\times\mathbb{R}$ equipped with a family of non-flat left-invariant Lorentzian metrics. We establish a complete classification and provide an explicit geometric characterization of all parallel and totally geodesic hypersurfaces within these spaces.
Abstract
This paper investigates the four-dimensional 2-step nilpotent Lie group $H_{3}\times\mathbb{R}$ equipped with a family of non-flat left-invariant Lorentzian metrics. We establish a complete classification and provide an explicit geometric characterization of all parallel and totally geodesic hypersurfaces within these spaces.
관련 논문AI추천
Classification of homogeneous structures on 4-dimensional nilpotent Lie groupsRabea Taleb, Wafaa Batat대한수학회 · 대한수학회지2025 · 제62권 제1호Left invariant Lorentzian metrics and curvatures on non-unimodular Lie groups of dimension three이종범, 하구용대한수학회 · 대한수학회지2023 · 제60권 제1호Homogeneous structures on four-dimensional Lorentzian Damek-Ricci spacesAssia Mostefaoui, Noura Sidhoumi대한수학회 · 대한수학회논문집2023 · 제38권 제1호Four-dimensional Naturally Reductive Pseudo-Riemannian Homogeneous SpacesBarbara De Leo경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2012 · 제52권 제1호Nilpotency of the Ricci operator of pseudo-Riemannian solvmanifoldsHuihui An, Shaoqiang Deng, Zaili Yan대한수학회 · 대한수학회보2024 · 제61권 제3호GEODESIC FORMULA OF A CERTAIN CLASS OF PSEUDORIEMANNIAN 2-STEP NILPOTENT GROUPS AND JACOBI OPERATORS ALONG GEODESICS IN PSEUDORIEMANNIAN 2-STEP NILPOTENT GROUPS박건, 장창림, B. Min영남수학회 · East Asian Mathematical Journal2010 · 제26권 제5호
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