• Kyungpook Mathematical Journal
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• 제58권2호
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• pp.347-359
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• 2018

A Kenmotsu manifold $M^n({\phi},\;{\xi},\;{\eta},\;g)$, (n = 2m + 1 > 3) is called a generalized ${\phi}-recurrent$ if its curvature tensor R satisfies $${\phi}^2(({\nabla}_wR)(X,Y)Z)=A(W)R(X,Y)Z+B(W)G(X,Y)Z$$ for all $X,\;Y,\;Z,\;W{\in}{\chi}(M)$, where ${\nabla}$ denotes the operator of covariant differentiation with respect to the metric g, i.e. ${\nabla}$ is the Riemannian connection, A, B are non-vanishing 1-forms and G is given by G(X, Y)Z = g(Y, Z)X - g(X, Z)Y. In particular, if A = 0 = B then the manifold is called a ${\phi}-symmetric$. Now, a Kenmotsu manifold $M^n({\phi},\;{\xi},\;{\eta},\;g)$, (n = 2m + 1 > 3) is said to be generalized ${\phi}-Ricci$ recurrent if it satisfies $${\phi}^2(({\nabla}_wQ)(Y))=A(X)QY+B(X)Y$$ for any vector field $X,\;Y{\in}{\chi}(M)$, where Q is the Ricci operator, i.e., g(QX, Y) = S(X, Y) for all X, Y. In this paper, we study generalized ${\phi}-recurrent$ and generalized ${\phi}-Ricci$ recurrent Kenmotsu manifolds with respect to quarter-symmetric metric connection and obtain a necessary and sufficient condition of a generalized ${\phi}-recurrent$ Kenmotsu manifold with respect to quarter symmetric metric connection to be generalized Ricci recurrent Kenmotsu manifold with respect to quarter symmetric metric connection.

• 한국실내디자인학회논문집
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• 제11호
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• pp.57-63
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• 1997

In the early 20'c, scientific thoughts make a change the absolute and separate concept of space-time into relative concept of continual entity; a kind of ideal world. It suggests that the meaning of geometry as absolute truth with which has endowed human beings would changed to a relative meaning of accumulation in intellectual work on 'nature'. This cognitive changes appeared into absolute arts in 20'c like Cubism, Superematism or Constructivism. De Stijl movement which had recepted the relative concepts like Einstein's 'theory of relativity' as a developed thought from Newton-Cartesian cognition on the world. Abstration would be adequate method for expressing the dynamics and interrelationship between forms and for giving values to indivisual elements in a compositiov. This method had appeared Modern architectural form, as a common framework. The expression characteristics of geometrical design in Deconstructive and Experimental architecture were summerized in four features through the results of the analysis. First, the relation of architectural element and intertextuality is expressed in discontinuation of context and refusal of functional building. Second, the concept of trace expresses as connection of place, decomposing of excavation of trace, trace of axis, trace of fragments. Third, anti-gravity expression is there to express of open cubic, to outgrow of rectangular system, to outgrow of volume, to separate of ground connectiov. Fourth, the complex composition of abstracted geometric form is these to abstracted geometry about indefinite shape, to layer through the overlap and collage, to de-meaning and amusement of form through the pursuit of uncertainty, to indeterminate of formal meaning through operation and composition of similar form cause to the diverse of meaning.

• 복식
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• 제60권3호
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• pp.26-43
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• 2010

The inflow of digital technology into the art, especially in the Fashion Illustration since 1990, makes the new aesthetics of the beginning of the 21 century which the Software aesthetics can be called. The meeting of technology and the art make us recall a great scientist and artist, Leonardo da Vinci in the Renaissance that the notion of the art and skill was unified, same as the ancient history. This study is purposed to expand the concept of the art for the broad exchange of the digital technology and art and for the extensive expression method of the modern fashion illustration. Having views on science theory of the beginning of the 20 century, Theory of Relativity which had given a lot of influence in the philosophy, the litterature and the art, as well as all the science, it makes a connection with the history of art in the beginning of the 20 century and the story of the digital art in the beginning of the 21 century. Firstly, the Fauvism and 2D is based on the expression of the glowing and bright color by the Principle of constancy of light velocity. Secondly, the Cubism and 3D is associated with the Special theory of relativity in the cyberspace which the space and the time are totally accorded. Thirdly, the Futurism and 4D is compared with the General theory of relativity which contains the material and the gravity. They are gradually evolved into the Interactive art and the Kinetic art by the digital technology in the profound cyberspace.