Background. Women with polycystic ovary syndrome (PCOS) could develop subclinical atherosclerosis during life. Purpose. To analyze cardiovascular risk (CVR) factors and their relation to clinical markers of cardiovascular disease (CVD) in respect to their age. Material and Methods. One hundred women with PCOS (26.32 ± 5.26 years, BMI: 24.98 ± 6.38 kg/m2) were compared to 50 respective controls. In all subjects, total cholesterol (TC), HDL-C, LDL-C, triglycerides, TC/HDL-C and TG/HDL-C ratios, glucose, insulin and HOMA index, waist-to-hip ratio (WHR), systolic and diastolic blood pressure (SBP and DBP, resp.), and carotid intima-media thickness (CIMT) were analyzed in respect to their age and level of androgens. Results. PCOS over 30 years had higher WHR (P = 0.008), SBP (P < 0.001), DBP (P < 0.001), TC (P = 0.028), HDL-C (P = 0.028), LDL-C (P = 0.045), triglycerides (P < 0.001), TC/HDL-C (P < 0.001), and triglycerides/HDL-C (P < 0.001) and had more prevalent hypertension and pronounced CIMT on common carotid arteries even after adjustment for BMI (P = 0.005 and 0.036, resp.). TC/HDL-C and TG/HDL-C were higher in PCOS with the highest quintile of FAI in comparison to those with lower FAI (P = 0.045 and 0.034, resp.). Conclusions. PCOS women older than 30 years irrespective of BMI have the potential for early atherosclerosis mirrored through the elevated lipids/lipid ratios and through changes in blood pressure.
Two metrics on a manifold are geodesically equivalent if sets of their unparameterized geodesics coincide. In this paper we show that if two left G-invariant metrics of arbitrary signature on homogenous space G/H are geodesically equivalent, they are affinely equivalent, i.e. they have the same Levi-Civita connection. We also prove that existence of non-proportional, geodesically equivalent, G-invariant metrics on homogenous space G/H implies that their holonomy algebra cannot be full. We give an algorithm for finding all left invariant metrics geodesically equivalent to a given left invariant metric on a Lie group. Using that algorithm we prove that no two left invariant metric, of any signature, on sphere S 3 are geodesically equivalent. However, we present examples of Lie groups that admit geodesically equivalent, non-proportional, left-invariant metrics.
In this paper the complete classification of left invariant metrics of
arbitrary signature on solvable Lie groups is given. By identifying the Lie
algebra with the algebra of left invariant vector fields on the
corresponding Lie group ??, the inner product ??,?? on g = Lie G extends
uniquely to a left invariant metric ?? on the Lie group. Therefore, the
classification problem is reduced to the problem of classification of pairs
(g, ??,??) known as the metric Lie algebras. Although two metric algebras
may be isometric even if the corresponding Lie algebras are non-isomorphic,
this paper will show that in the 4-dimensional solvable case isometric means
isomorphic. Finally, the curvature properties of the obtained metric
algebras are considered and, as a corollary, the classification of flat,
locally symmetric, Ricciflat, Ricci-parallel and Einstein metrics is also
given.
UDC 514
We give the full classification of left-invariant metrics of an arbitrary signature on the Lie group corresponding to the real hyperbolic space. We show that all metrics have constant sectional curvature and that they are geodesically complete only in the Riemannian case.
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