Bu çalışmada, ilk olarak 4-boyutlu Öklidyen uzayında bir Monge hiperyüzeyinin ortalama ve Gaussian eğriliklerini verdik. Ardından, farklı yoğunluklara sahip uzayında Monge hiperyüzeylerini çalıştık. Bu bağlamda, ve hepsi aynı anda sıfır olmayan sabitler olmak üzere, (lineer yoğunluk) ve yoğunluklu uzayında ağırlıklı minimal ve ağırlıklı flat Monge hiperyüzeylerini ve sabitlerinin farklı seçimleri yardımıyla elde ettik. Anahtar Kelimeler:Yoğunluklu manifold, ağırlıklı ortalama eğrilik, ağırlıklı gaussian eğriliği, monge yüzeyleri.
Rotational hypersurfaces in Euclidean 4-space with density have considered. Weighted minimal and weighted flat rotational hypersurfaces in Euclidean 4-space with density have obtained. Some examples for these hypersurfaces have constructed.
The object of the present paper is to classify N(κ)-contact metric manifolds admitting the semi-symmetric non-metric connection with certain curvature conditions the projectively curvature tensor. We studied projective flat, ξ −projectively flat, φ −projectively flat N(κ)contact metric manifolds admitting the semi-symmetric non-metric connection. Also, we examine such manifolds under some local symmetry conditions related to projective curvature tensor.
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