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Warped product pseudo-slant submanifolds of a Kenmotsu manifold
Mohammad Shuaib 대한수학회 2023 대한수학회논문집 Vol.38 No.2
For a pseudo-slant submanifold of a Kenmotsu manifold, we have worked out conditions in terms its canonical structure tensors, $T$ and $F$, and its shape operator so that it reduces to a warped product submanifold.
CONFORMAL HEMI-SLANT SUBMERSION FROM KENMOTSU MANIFOLD
( Mohammad Shuaib ),( Tanveer Fatima ) 호남수학회 2023 호남수학학술지 Vol.45 No.2
As a generalization of conformal semi-invariant submersion, conformal slant submersion and conformal semi-slant submersion, in this paper we study conformal hemi-slant submersion from Kenmotsu manifold onto a Riemannian manifold. The necessary and sufficient conditions for the integrability and totally geodesicness of distributions are discussed. Moreover, we have obtained sufficient condition for a conformal hemi-slant submersion to be a homothetic map. The condition for a total manifold of the submersion to be twisted product is studied, followed by other decomposition theorems.
Mutational Analysis of Prohibitin - A Highly Conserved Gene in Indian Female Breast Cancer Cases
Najm, Mohammad Zeeshan,Akhtar, Md. Salman,Ahmad, Istaq,Sadaf, Sadaf,Mallick, Mohd Nasar,Kausar, Mohd Adnan,Chattopadhyay, Shilpi,Ahad, Amjid,Zaidi, Shuaib,Husain, Syed Akhtar,Siddiqui, Waseem Ahmad Asian Pacific Journal of Cancer Prevention 2012 Asian Pacific journal of cancer prevention Vol.13 No.10
Prohibitin (PHB) is a chaperone protein which is highly conserved evolutionarily. It shows significant homology with the Drosophila cc gene which is considered important for development and differentiation of Drosophila melanogaster. Investigations have revealed an involvement of PHB in cellular proliferation and development, apoptosis, signal transduction, mitochondrial function and regulation of the estrogen and androgen receptors. Therefore, we conducted the present study to analyze mutations in the highly conserved region in Indian female breast cancer patients. Conventional PCR-SSCP and Automated DNA sequencing were performed with a total of 105 breast cancer samples along with adjacent normal tissue. Of the total, 14.2% (15/105) demonstrated a mutation status of prohibitin observed in our study population. We identified a novel missense mutation (Thr>Ser), a novel deletion of T nucleotide in an intron adjacent to intron-exon boundary and a previously determined missense mutation (Val>Ala). A statistically significant correlation was obtained which suggested that prohibitin may be associated with tumor development and/or progression of at least some proportion of breast cancers.
Characterizations of Lie Triple Higher Derivations of Triangular Algebras by Local Actions
Ashraf, Mohammad,Akhtar, Mohd Shuaib,Jabeen, Aisha Department of Mathematics 2020 Kyungpook mathematical journal Vol.60 No.4
Let ℕ be the set of nonnegative integers and 𝕬 be a 2-torsion free triangular algebra over a commutative ring ℛ. In the present paper, under some lenient assumptions on 𝕬, it is proved that if Δ = {𝛿<sub>n</sub>}<sub>n∈ℕ</sub> is a sequence of ℛ-linear mappings 𝛿<sub>n</sub> : 𝕬 → 𝕬 satisfying ${\delta}_n([[x,\;y],\;z])\;=\;\displaystyle\sum_{i+j+k=n}\;[[{\delta}_i(x),\;{\delta}_j(y)],\;{\delta}_k(z)]$ for all x, y, z ∈ 𝕬 with xy = 0 (resp. xy = p, where p is a nontrivial idempotent of 𝕬), then for each n ∈ ℕ, 𝛿<sub>n</sub> = d<sub>n</sub> + 𝜏<sub>n</sub>; where d<sub>n</sub> : 𝕬 → 𝕬 is ℛ-linear mapping satisfying $d_n(xy)\;=\;\displaystyle\sum_{i+j=n}\;d_i(x)d_j(y)$ for all x, y ∈ 𝕬, i.e. 𝒟 = {d<sub>n</sub>}<sub>n∈ℕ</sub> is a higher derivation on 𝕬 and 𝜏<sub>n</sub> : 𝕬 → Z(𝕬) (where Z(𝕬) is the center of 𝕬) is an ℛ-linear map vanishing at every second commutator [[x, y], z] with xy = 0 (resp. xy = p).
SOME WARPED PRODUCT SUBMANIFOLDS OF A KENMOTSU MANIFOLD
Khan, Viqar Azam,Shuaib, Mohammad Korean Mathematical Society 2014 대한수학회보 Vol.51 No.3
Many differential geometric properties of a submanifold of a Kaehler manifold are conceived via canonical structure tensors T and F on the submanifold. For instance, a CR-submanifold of a Kaehler manifold is a CR-product if and only if T is parallel on the submanifold (c.f. [2]). Warped product submanifolds are generalized version of CR-product submanifolds. Therefore, it is natural to see how the non-triviality of the covariant derivatives of T and F gives rise to warped product submanifolds. In the present article, we have worked out characterizations in terms of T and F under which a contact CR- submanifold of a Kenmotsu manifold reduces to a warped product submanifold.
Some warped product submanifolds of a Kenmotsu manifold
Viqar Azam Khan,Mohammad Shuaib 대한수학회 2014 대한수학회보 Vol.51 No.3
Many differential geometric properties of a submanifold of a Kaehler manifold are conceived via canonical structure tensors T and F on the submanifold. For instance, a CR-submanifold of a Kaehler mani- fold is a CR-product if and only if T is parallel on the submanifold (c.f. [2]). Warped product submanifolds are generalized version of CR-product submanifolds. Therefore, it is natural to see how the non-triviality of the covariant derivatives of T and F gives rise to warped product subman- ifolds. In the present article, we have worked out characterizations in terms of T and F under which a contact CR- submanifold of a Kenmotsu manifold reduces to a warped product submanifold.