• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.629-641
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• 2023

The aim of this paper is two-fold. First, we study the Chinea-Gonzalez class C₁₂ of almost contact metric manifolds and we discuss some fundamental properties. We show there is a one-to-one correspondence between C₁₂ and Kählerian structures. Secondly, we give some basic results for Riemannian curvature tensor of C₁₂-manifolds and then establish equivalent relations among 𝜑-sectional curvature. Concrete examples are given.

• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.1019-1045
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• 2006

As a natural generalization of a Sasakian space form, we define a contact strongly pseudo-convex CR-space form (of constant pseudo-holomorphic sectional curvature) by using the Tanaka-Webster connection, which is a canonical affine connection on a contact strongly pseudo-convex CR-manifold. In particular, we classify a contact strongly pseudo-convex CR-space form $(M,\;\eta,\;\varphi)$ with the pseudo-parallel structure operator $h(=1/2L\xi\varphi)$, and then we obtain the nice form of their curvature tensors in proving Schurtype theorem, where $L\xi$ denote the Lie derivative in the characteristic direction $\xi$.