### $(m+1)$-dimensional spacelike parallel ${p}_{i}$-equidistant ruled surfaces in the Minkowski space ${R}_{1}^{n}$.

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In the class of real hypersurfaces ${M}^{2n-1}$ isometrically immersed into a nonflat complex space form ${\tilde{M}}_{n}\left(c\right)$ of constant holomorphic sectional curvature $c$$(\ne 0)$ which is either a complex projective space $\u2102{P}^{n}\left(c\right)$ or...

We study affine nondegenerate Blaschke hypersurfaces whose shape operators are parallel with respect to the induced Blaschke connections. We classify such surfaces and thus give an exact classification of extremal locally symmetric surfaces, first described by F. Dillen.

We review some techniques from the Möbius geometry of curves and surfaces in the 3-sphere, consider canal surfaces using their characteristic circles, and express the conformal curvature, and conformal torsion, of a vertex-free space curve in terms of its corresponding curve of osculating circles, and osculating spheres, respectively. We accomplish all of this strictly within the framework of Möbius geometry, and compare our results with the literature. Finally, we show how our formulation allows...

We classify nonminimal biminimal Legendrian surfaces in 5-dimensional Sasakian space forms.