Final answer:
The three names for the connections next to the lesser omentum include the hepatoduodenal ligament, the hepatogastric ligament, and the bile duct. They are essential for the vascular and biliary anatomy of the liver and the gastrointestinal tract.
Step-by-step explanation:
The three names for the connections next to the lesser omentum are the hepatoduodenal ligament, the hepatogastric ligament, and the bile duct, along with the hepatic artery and portal vein. The lesser omentum is a significant peritoneal fold that suspends the stomach from the inferior border of the liver and provides a pathway for structures connecting to the liver. It plays a critical role in the structure and function of the upper abdomen, with relations to the pancreas, small intestine, appendix, and mesenteric artery. The hepatoduodenal ligament contains the portal triad consisting of the common bile duct, the hepatic artery, and the portal vein. These structures are essential for the vascular and biliary anatomy of the liver and the gastrointestinal tract.