Ruled real hypersurfaces in the complex hyperbolic quadric

• Autorzy: Lee Hyunjin , Suh Young Jin , Woo Changhwa

Identyfikatory

DOI

10.1515/dema-2023-0258

• Języki publikacji: EN

Abstrakty

EN

In this article, we introduce a new family of real hypersurfaces in the complex hyperbolic quadric [formula] , namely, the ruled real hypersurfaces foliated by complex hypersurfaces. Berndt described an example of such a real hypersurface in [formula] as a homogeneous real hypersurface generated by a [symbol] -principal horocycle in a real form [formula]. So, in this article, we compute a detailed expression of the shape operator for ruled real hypersurfaces in [formula] and investigate their characterizations in terms of the shape operator and the integrable distribution [formula]. Then, by using these observations, we give two kinds of classifications of real hypersurfaces in [formula] satisfying η -parallelism under either η -commutativity of the shape operator or integrability of the distribution C. Moreover, we prove that the unit normal vector field of a real hypersurface with η -parallel shape operator in [formula] is [symbol] -principal. On the other hand, it is known that all contact real hypersurfaces in [formula] have a [symbol] -principal normal vector field. Motivated by these results, we give a characterization of contact real hypersurfaces in [formula] in terms of η -parallel shape operator.

Słowa kluczowe

EN

ruled real hypersurface; η-parallel shape operator; η-commuting shape operator; singular vector fields; complex hyperbolic quadric

PL

hiperpowierzchnia rzeczywista; operator kształtu; pola wektorowe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2023
• Tom: Vol. 56, nr 1
• Strony: art. no. 20230258
• Opis fizyczny: Bibliogr. 28 poz., tab.

Twórcy

autor

Lee Hyunjin

• Department of Mathematics Education, Chosun University, Gwangju 61452, Republic of Korea

autor

Suh Young Jin

• Department of Mathematics and Research Institute of Real and Complex Manifolds, Kyungpook National University, Daegu 41566, Republic of Korea

autor

Woo Changhwa

• Department of Applied Mathematics, Pukyong National University, Busan 48547, Republic of Korea

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).