Classification of hypersurfaces in the four dimensional thurston geometry $Sol_{m,n}^4$

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2025年7月21日

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Mohamed Belkhelfa,
Hichem Mokni

摘要

This paper investigates hypersurfaces in the four-dimensional Thurston geometry $Sol^4_{m,n}$ $S o l_{m, n}^{4}$ . We present a complete classification of hypersurfaces whose second fundamental form satisfies the Codazzi tensor condition, encompassing both totally geodesic hypersurfaces and parallel hypersurfaces. Furthermore, we give a classification of totally umbilical hypersurfaces of $Sol^4_{m,n}$ $S o l_{m, n}^{4}$ .

Classification of hypersurfaces in the four dimensional thurston geometry \(Sol_{m,n}^4\)

摘要