Characterizing Base in Warped Product Submanifolds of Complex Projective Spaces by Differential Equations

In this study, a link between the squared norm of the second fundamental form and the Laplacian of the warping function for a warped product pointwise semi-slant submanifold Mn in a complex projective space is presented. Some characterizations of the base NT of Mn are offered as applications. We also look at whether the base NT is isometric to the Euclidean space Rp or the Euclidean sphere Sp, subject to some constraints on the second fundamental form and warping function.

Bounds for Statistical Curvatures of Submanifolds in Kenmotsu-like Statistical Manifolds

In this article, we obtain certain bounds for statistical curvatures of submanifolds with any codimension of Kenmotsu-like statistical manifolds. In this context, we construct a class of optimum inequalities for submanifolds in Kenmotsu-like statistical manifolds containing the normalized scalar curvature and the generalized normalized Casorati curvatures. We also define the second fundamental form of those submanifolds that satisfy the equality condition. On Legendrian submanifolds of Kenmotsu-like statistical manifolds, we discuss a conjecture for Wintgen inequality. At the end, some immediate geometric consequences are stated.

Surfaces of Finite III-type in the Euclidean 3-Space

In this paper, we firstly investigate some relations regarding the first and the second Laplace operators corresponding to the third fundamental form III of a surface in the Euclidean space E3. Then, we introduce the finite Chen type surfaces of revolution with respect to the third fundamental form which Gauss curvature never vanishes.

Streben of the I as the Fundamental Form of Consciousness

This paper aims to show that Fichte’s concept of Streben or striving of the I is the necessary condition of finite or individual consciousness. The I posits itself absolutely, but in doing so it posits the not-I as well, therefore it posits itself absolutely as self-limiting I. If there was no limitation on the infinite striving of the I’s activity, then there would be no I, at least as we know it. Firstly, the paper emphasizes why this activity or striving needs to be infinite, and at the same time determined. Then, why is it necessary for theoretical self-consciousness, regarding the idea of Anstoss, divided self and absolute I. Finally, why is it also necessary for practical standpoint, considering the ideas of practical striving, tendency, longing, drive, and desire (both in individual striving towards self-coherence and social drive for intersubjectivity). It will be concluded that the I possesses a “dual nature” or divided character: it is finite, but it strives towards infinity. The tension arising from this contradiction should be the moving force of the I.

Surfaces of Finite III-type

In this paper, we consider surfaces of revolution in the 3-dimensional Euclidean space E3 with nonvanishing Gauss curvature. We introduce the finite Chen type surfaces with respect to the third fundamental form of the surface. We present a special case of this family of surfaces of revolution in E3, namely, surfaces of revolution with R is constant, where R denotes the sum of the radii of the principal curvature of a surface.

Talk About Structural Rationality

This chapter turns to the semantics of our ordinary talk about structural rationality. Such talk is typically conditional in form, and there is a challenge about whether it squares with the account of the fundamental form of the requirements of structural rationality defended in the previous chapter. Some have tried to meet this challenge by saying that ordinary conditional normative utterances express wide-scope claims, but this chapter argues that this theory is not semantically plausible. Instead, it shows how a standard contextualist semantics for modals and conditionals can vindicate the truth of ordinary conditional utterances about rationality and, indeed, how it can say that these utterances come out true in virtue of requirements of structural rationality of the kind defended in the previous chapter.

Hopf-type theorem for self-shrinkers

In this paper, we prove that a two-dimensional self-shrinker, homeomorphic to the sphere, immersed in the three-dimensional Euclidean space ℝ 3 {{\mathbb{R}}^{3}} is a round sphere, provided its mean curvature and the norm of the its position vector have an upper bound in terms of the norm of its traceless second fundamental form. The example constructed by Drugan justifies that the hypothesis on the second fundamental form is necessary. We can also prove the same kind of rigidity results for surfaces with parallel weighted mean curvature vector in ℝ n {{\mathbb{R}}^{n}} with radial weight. These results are applications of a new generalization of Cauchy’s Theorem in complex analysis which concludes that a complex function is identically zero or its zeroes are isolated if it satisfies some weak holomorphy.

Create a Sensuousness Space of Installation a Sense of Introspection Sculpture created by Internalizing Islamic Geometrical Ornament found in National Mosque

This project seeks to identify the fundamental form of Islamic geometrical patterns found in the National Mosque. The internalization from the subject and visit helps to produce an installation sculpture. The sculpting process uses plywood as the primary material and is formed by using mathematical methods and woodworking as the approach. The work presents in installation as it potentially delivers a sense of sacredness towards the audience. Therefore, this study explores the chronology of artmaking inspired by the hidden form and its foundation in Islamic ornament and reviews how its complexity creates a sense of sacredness towards the atmosphere of human psychology. Keywords: Sensuousness Space, Islamic Geometrical Ornament, National Mosque, Installation eISSN: 2398-4287 © 2021. The Authors. Published for AMER ABRA cE-Bs by e-International Publishing House, Ltd., U.K. This is an open access article under the CC BYNC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer–review under responsibility of AMER (Association of Malaysian Environment-Behaviour Researchers), ABRA (Association of Behavioural Researchers on Asians) and cE-Bs (Centre for Environment-Behaviour Studies), Faculty of Architecture, Planning & Surveying, Universiti Teknologi MARA, Malaysia. DOI: https://doi.org/10.21834/ebpj.v6iSI6.3042

Complete 3-dimensional λ-translators in the Euclidean space ℝ4

In this paper, we obtain the classification theorems for 3-dimensional complete [Formula: see text]-translators [Formula: see text] with constant squared norm [Formula: see text] of the second fundamental form and constant [Formula: see text] in the Euclidean space [Formula: see text].