• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.31-46
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• 2009

In this paper we study the geometry of Einstein half light like submanifolds M of a Lorentz manifold ($\bar{M}$(c), $\bar{g}$) of constant curvature c, equipped with an integrable screen distribution on M such that the induced connection ${\nabla}$ is a metric connection and the operator $A_u$ is a screen shape operator.

• The Pure and Applied Mathematics
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• v.27 no.3
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• pp.109-124
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• 2020

We establish coincidence point theorem for S-non-decreasing mappings under Geraghty-type contraction on partially ordered metric spaces. With the help of obtain result, we derive two dimensional results for generalized compatible pair of mappings F, G : X² → X. As an application, we obtain the solution of integral equation and also give an example to show the usefulness of our results. Our results improve, sharpen, enrich and generalize various known results.

• The Pure and Applied Mathematics
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• v.22 no.4
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• pp.359-364
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• 2015

We present smooth simply connected closed 4k-dimensional manifolds N := N_k, for each k ∈ {2, 3, ⋯}, with distinct symplectic deformation equivalence classes [[ω_i]], i = 1, 2. To distinguish [[ω_i]]’s, we used the symplectic Z invariant in [4] which depends only on the symplectic deformation equivalence class. We have computed that Z(N, [[ω₁]]) = ∞ and Z(N, [[ω₂]]) < 0.

• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.281-288
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• 2012

In this paper, the author defines a new generalized ${\eta}$, ${\delta}$, ${\alpha}$)-pseudomonotone mapping and considers the equivalence of Stampacchia-type vector variational-like inequality problems and Minty-type vector variational-like inequality problems for generalized (${\eta}$, ${\delta}$, ${\alpha}$)-pseudomonotone mappings in Banach spaces, called the generalized vector Minty's lemma.

• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.239-249
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• 2012

For each submanifold X in the sphere $S^n$; we show that the corresponding conormal bundle $N^*X$ is Lagrangian for the Stenzel form on $T^*S^n$. Furthermore, we correspond an austere submanifold X to a special Lagrangian submanifold $N^*X$ in $T^*S^n$. We also discuss austere submanifolds in $S^n$ from isoparametric geometry.

• The Pure and Applied Mathematics
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• v.10 no.2
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• pp.119-126
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• 2003

In this paper, when N is a compact Riemannian manifold, we considered the positive time solution to equation $\Box_gu(t,x)-c_nu(t,x)+c_nu(t,x)^{(n+3)/(n-1)}$ on M ＝$(-{\infty},+{\infty})\;{\times}_f\;N$, where $c_n$ ＝(n－1)/4n and $\Box_{g}$ is the d'Alembertian for a Lorentzian warped manifold.

• The Pure and Applied Mathematics
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• v.10 no.3
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• pp.145-161
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• 2003

Weak commutativity of a pair of maps was introduced by Sessa [On a weak commutativity condition of mappings in fixed point considerations. Publ. Inst. Math. (Beograd) (N.S.) 32(40) (1982),149-153] in fixed point considerations. Thereafter a number of generalizations of this notion has been obtained. The purpose of this paper is to present a brief development of weaker forms of commuting maps, and to obtain two fixed point theorems for noncommuting and noncontinuous maps on noncomplete metric spaces.

• The Pure and Applied Mathematics
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• v.3 no.1
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• pp.73-81
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• 1996

Multiple objective programming has been a popular research area since 1970. The pervasiveness of multiple objective in decision problems have led to explosive growth during the 1980's. Several approaches (interactive methods, feasible direction methods, criterion weight space methods, Lagrange multiplies methods, etc) have been developed for solving decision problems having multiple objectives. However there are still many mathematically challengings including multiple objective integer, nonlinear optimization problems which require further mathematically oriented research. (omitted)

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1367-1382
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• 2020

We study rigidity results for the Einstein metrics as the critical points of a family of known quadratic curvature functionals involving the scalar curvature, the Ricci curvature and the Riemannian curvature tensor, characterized by some pointwise inequalities involving the Weyl curvature and the traceless Ricci curvature. Moreover, we also provide a few rigidity results for locally conformally flat critical metrics.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1525-1537
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• 2019

Let ${\tilde{M}}$ be a Riemannian manifold equipped with a concircular vector field ${\tilde{X}}$ and M a submanifold (with its induced metric) of ${\tilde{M}}$. Denote by X the restriction of ${\tilde{X}}$ on M and by $X^T$ the tangential component of X, called the canonical field of M. In this article we study submanifolds of ${\tilde{M}}$ whose canonical field $X^T$ is also concircular. Several characterizations and classification results in this respect are obtained.