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BI-ROTATIONAL HYPERSURFACE SATISFYING ∆IIIx =AxIN 4-SPAC
Erhan Guler,Yusuf Yaylı,,Hasan Hilmi Hacısalihoglu 호남수학회 2022 호남수학학술지 Vol.44 No.2
We examine the bi-rotational hypersurface x = x(u, v, w) with the third Laplace-Beltrami operator in the four dimensional Euclidean space E 4. Giving the i-th curvatures of the hypersurface x, we obtain the third Laplace-Beltrami operator of the bi-rotational hypersurface satisfying ∆IIIx =Ax for some 4 × 4 matrix A.
Geometric applications and kinematics of umbrella matrices
Mert Çarboğa,Yusuf Yaylı 강원경기수학회 2023 한국수학논문집 Vol.31 No.3
This paper introduces a novel method for obtaining umbrella matrices, which are defined as orthogonal matrices with row sums of one, using skew-symmetric matrices and Cayley’s Formula. This method is presented for the first time in this paper. We also investigate the kinematic properties and applications of umbrella matrices, demonstrating their usefulness as a tool in geometry and kinematics. Our findings provide new insights into the connections between matrix theory and geometric applications.