Search

Since a planar periodic transmission line can suppress drastically the electromagnetic coupling, it would be advantageous to use such a kind of transmission lines in solving the problem of miniaturization of circuit area. By adjusting the lattice constants and geometric parameters of periodic microstrip lines, a time domain characteristic impedance that is the same as that of conventional microstrip lines (CMLs) can be achieved. Such periodic microstrip lines can therefore be used to trick high-speed digital signals, causing a digital signal to misjudge the time domain characteristic impedance of the transmission lines. The theoretical analysis has been verified by our experimental measurement results. Besides, a specific expression for the characteristic impedance of lossless periodic artificial materials is deduced by a circuit model and a standard of misidentification for the characteristic impedance of periodic microstrip lines is given for the digital signals. [ABSTRACT FROM AUTHOR]

Cartan hypersurfaces are minimal isoparametric hypersurfaces with 3 distinct constant principal curvatures in unit spheres. In this article, we firstly build a relationship between the focal submanifolds of Cartan hypersurfaces and the Hopf fiberations and give a new proof of the classification result on Cartan hypersurfaces. Nextly, we show that there exists a Riemannian submersion with totally geodesic fibers from each Cartan hypersurface M to the projective planes $${{\mathbb{F}}P^2}$$ ( $${{\mathbb{F}}={\mathbb{R}},{\mathbb{C}},{\mathbb{H}},{\mathbb{O}}}$$ for m = 1, 2, 4, 8, respectively) endowed with the canonical metrics. As an application, we give several interesting examples of Riemannian submersions satisfying a basic equality due to Chen (Proc Jpn Acad Ser A Math Sci 81:162-167, 2005). [ABSTRACT FROM AUTHOR]

The focal submanifolds of isoparametric hypersurfaces in spheres are all minimal Willmore submanifolds, mostly being $${\mathcal{A}}$$ -manifolds in the sense of A.Gray but rarely Ricci-parallel, see Li et al. (Sci China Math 58, 2015), Qian et al. (Ann Glob Anal Geom 43:47-62, 2013), Tang and Yan (Isoparametric foliation and a problem of Besse on generalizations of Einstein condition , 2013). In this paper we study the geometry of the focal submanifolds via Simons formula. We show that all the focal submanifolds with g ≥ 3 are not normally flat by estimating the normal scalar curvatures. Moreover, we give a complete classification of the semiparallel submanifolds among the focal submanifolds. [ABSTRACT FROM AUTHOR]

A-manifolds and B-manifolds, introduced by Gray (1978), are two significant classes of Einstein-like Riemannian manifolds. A Riemannian manifold is Ricci parallel if and only if it is simultaneously an A-manifold and a B-manifold. The present paper proves that both focal submanifolds of each isoparametric hypersurface in unit spheres with g = 4 distinct principal curvatures are A-manifolds. As for the focal submanifolds with g = 6, m = 1 or 2, only one is an A-manifold, and neither is a B-manifold. [ABSTRACT FROM AUTHOR]