• Journal of the Korean Mathematical Society
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• v.21 no.1
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• pp.21-29
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• 1984

• The Mathematical Education
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• v.33 no.1
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• pp.103-114
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• 1994

• The Mathematical Education
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• v.13 no.2
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• pp.32-33
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• 1974

• Kyungpook Mathematical Journal
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• v.17 no.2
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• pp.227-233
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• 1977

• Journal of the Korean Mathematical Society
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• v.39 no.2
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• pp.237-252
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• 2002

We study the compatibility conditions and the existence of solutions or overdetermined PDE systems that admit complete prolongation. For a complete system of order k there exists a submanifold of the ($\kappa$-1)st jet space of unknown functions that is the largest possible set on which the initial conditions of ($\kappa$-1)st order may take values. There exists a unique solution for any initial condition that belongs to this set if and only if the complete system satisfies the compatibility conditions on the initial data set. We prove by applying the Frobenius theorem to a Pfaffian differential system associated with the complete prolongation.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.455-463
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• 2010

The differentiable manifold with f - structure were studied by many authors, for example: K. Yano [7], Ishihara [8], Das [4] among others but thus far we do not know the geometry of manifolds which are endowed with special polynomial $F_{a(j){\times}(j)$-structure satisfying $$\prod\limits_{j=1}^{k}\;[F^2+a(j)F+\lambda^2(j)I]\;=\;0$$ However, special quadratic structure manifold have been defined and studied by Sinha and Sharma [8]. The purpose of this paper is to study the geometry of differentiable manifolds equipped with such structures and define special polynomial structures for all values of j = 1, 2,$\ldots$,$K\;\in\;N$, and obtain integrability conditions of the distributions $\pi_m^j$ and ${\pi\limits^{\sim}}_m^j$.

• East Asian mathematical journal
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• v.38 no.5
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• pp.643-647
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• 2022

Let F² denote the space of entire functions f on ℂ that are square integrable with respect to the Gaussian measure $dG(z)={\frac{1}{\pi}}{e^{-{\mid}z{\mid}^2}}$, where dA(z) = dxdy is the ordinary area measure. The Fock-Dirichlet space $F^2_{\mathcal{D}}$ consists of all entire functions f with f' ∈ F². We estimate Taylor coefficients of functions in the Fock-Dirichlet space. The Fock-Nevanlinna space $F^2_{\mathcal{N}}$ consists of entire functions that possesses just a bit more integrability than square integrability. In this note we prove that $F^2_{\mathcal{D}}=F^2_{\mathcal{N}}$.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.475-490
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• 2022

The main purpose of the present paper is to introduce a brief analysis on some properties of quasi hemi-slant submanifolds of Kenmotsu manifolds. After discussing the introduction and some preliminaries about the Kenmotsu manifold, we worked out some important results in the direction of integrability of the distributions of quasi hemi-slant submanifolds of Kenmotsu manifolds. Afterward, we investigate the conditions for quasi hemi-slant submanifolds of a Kenmotsu manifold to be totally geodesic and later we provide some non-trivial examples to validate the existence of such submanifolds.

• Journal of the Korean Mathematical Society
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• v.19 no.2
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• pp.111-116
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• 1983

• Communications of the Korean Mathematical Society
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• v.7 no.2
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• pp.279-291
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• 1992