• Kyungpook Mathematical Journal
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• v.20 no.1
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• pp.37-45
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• 1980

The Riemannian space of recurrent curvature was defined and studied by Ruse [8] and Walker [10]. In 1963, $M{\acute{o}}or$ [4] generalised this idea for Finsler spaces and defined and studied Finsler spaces of recurrent curvature. These spaces for various curvature tensors have subsequently been studied by Mishra and Pande [1], Sen [9] and Misra [3] etc. The purpose of the present paper is to study Finsler space based on the recurrency of the curvature tensors derived from non-linear connections.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.433-448
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• 2022

The Cartan's second curvature tensor Pⁱ_jkh is a positively homogeneous of degree-1 in yⁱ, where yⁱ represent a directional coordinate for the line element in Finsler space. In this paper, we discuss the decomposition of Cartan's second curvature tensor Pⁱ_jkh in two spaces, a generalized 𝔅P-recurrent space and generalized 𝔅P-birecurrent space. We obtain different tensors which satisfy the recurrence and birecurrence property under the decomposition. Also, we prove the decomposition for different tensors are non-vanishing. As an illustration of the applicability of the obtained results, we finish this work with some illustrative examples.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.177-186
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• 2017

In this paper, a type of Riemannian manifold (namely, pseudo semiconformally symmetric manifold) is introduced. Also the several geometric properties of such a manifold is investigated. Finally the existence of such a manifold is ensured by a proper example.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.593-607
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• 2021

The aim of the present paper is to establish an intrinsic generalization of Cartan connection in Finsler geometry. This connection is called the vertical recurrent Finsler connection. An intrinsic proof of the existence and uniqueness theorem for such connection is investigated. Moreover, it is shown that for such connection, the associated semi-spray coincides with the canonical spray and the associated nonlinear connection coincides with the Barthel connection. Explicit intrinsic expression relating this connection and Cartan connection is deduced. We also investigate some applications concerning the fundamental geometric objects associated with this connection. Finally, three important results concerning the curvature tensors associated to a special vertical recurrent Finsler connection are studied.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.319-329
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• 2014

In this paper we study the properties of conformally recurrent pseudo Riemannian manifolds admitting a proper conformal vector field with respect to the scalar field ${\sigma}$, focusing particularly on the 4-dimensional Lorentzian case. Some general properties already proven by one of the present authors for pseudo conformally symmetric manifolds endowed with a conformal vector field are proven also in the case, and some new others are stated. Moreover interesting results are pointed out; for example, it is proven that the Ricci tensor under certain conditions is Weyl compatible: this notion was recently introduced and investigated by one of the present authors. Further we study conformally recurrent 4-dimensional Lorentzian manifolds (space-times) admitting a conformal vector field: it is proven that the covector ${\sigma}_j$ is null and unique up to scaling; moreover it is shown that the same vector is an eigenvector of the Ricci tensor. Finally, it is stated that such space-time is of Petrov type N with respect to ${\sigma}_j$.

• The Journal of the Acoustical Society of Korea
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• v.42 no.4
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• pp.357-363
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• 2023

In underwater signal processing, separating individual signals from mixed signals has long been a challenge due to low signal quality. The common method using Short-time Fourier transform for spectrogram analysis has faced criticism for its complex parameter optimization and loss of phase data. We propose a Triple-path Recurrent Neural Network, based on the Dual-path Recurrent Neural Network's success in long time series signal processing, to handle three-dimensional tensors from multi-channel sensor input signals. By dividing input signals into short chunks and creating a 3D tensor, the method accounts for relationships within and between chunks and channels, enabling local and global feature learning. The proposed technique demonstrates improved Root Mean Square Error and Scale Invariant Signal to Noise Ratio compared to the existing method.