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Generalized Tri-recurrent Finsler Space Under Cartan-Type Mixed Covariant Derivatives
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In this paper, we concentrate on a new Finsler space that is a combination of two types of Cartan derivatives of third order for Berwald curvature tensor H_jkh^i. We find the condition that Berwald curvature tensor H_jkh^i is special generalized of generalized mixed trirecurrent. Furthermore, we show that the normal projective curvature tensor N_jkh^i is generalized hv- mixed trirecurrent if and only if the tensor ∂ ̇_j (H_hk-H_kh) behaves as mixed trirecurrent. Also, the Ricci tensor N_jk of the normal projective curvature tensor N_jkh^i is non – vanishing if and only if the tensor ((1-n) ∂ ̇_j ∂ ̇_k H+H_jk+H_kj) is mixed trirecurrent.
Title: Generalized Tri-recurrent Finsler Space Under Cartan-Type Mixed Covariant Derivatives
Description:
In this paper, we concentrate on a new Finsler space that is a combination of two types of Cartan derivatives of third order for Berwald curvature tensor H_jkh^i.
We find the condition that Berwald curvature tensor H_jkh^i is special generalized of generalized mixed trirecurrent.
Furthermore, we show that the normal projective curvature tensor N_jkh^i is generalized hv- mixed trirecurrent if and only if the tensor ∂ ̇_j (H_hk-H_kh) behaves as mixed trirecurrent.
Also, the Ricci tensor N_jk of the normal projective curvature tensor N_jkh^i is non – vanishing if and only if the tensor ((1-n) ∂ ̇_j ∂ ̇_k H+H_jk+H_kj) is mixed trirecurrent.
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