Introduction:
The Mongols were a nomadic people from the Central Asian steppes who created the largest land empire in history under the leadership of Genghis Khan. They were known for their military prowess and conquests, which included the invasion of India. However, among the mentioned Mongol leaders/commanders, Genghis Khan did not personally cross the Indus River to attack India.

Explanation:
Genghis Khan, born as Temujin, was the founder and first Great Khan of the Mongol Empire. He united the various Mongol tribes and launched a series of military campaigns that expanded the empire across Asia, Europe, and the Middle East. However, Genghis Khan did not directly lead an invasion into India.

Reasons why Genghis Khan did not invade India:
1. Focus on other regions: Genghis Khan had a vast empire to govern and manage, and he had to deal with numerous challenges and conquests. His primary focus was on consolidating his control over the areas he had already conquered and expanding into other regions like China, Central Asia, and the Middle East. India was not a priority for him.

2. Distance and geographical barriers: The Indus River served as a natural boundary between the Mongol Empire and the Indian subcontinent. Crossing the river would have required significant resources, logistics, and manpower, which Genghis Khan deemed unnecessary considering the other conquest opportunities available to him.

3. Lack of significant wealth and resources: Genghis Khan's military campaigns were often motivated by the desire for wealth and resources. India, although known for its rich culture and heritage, did not possess the same level of wealth and resources as regions like China and the Middle East. Therefore, it was not a lucrative target for Genghis Khan.

4. Lack of strategic importance: India, at that time, was divided into several small kingdoms and lacked a unified political structure. It did not pose a significant threat or challenge to the Mongol Empire. Genghis Khan preferred to focus on regions that had a more centralized power structure and posed a greater strategic advantage.

Conclusion:
While the Mongols under Genghis Khan were known for their military conquests, Genghis Khan himself did not personally lead an invasion into India. The reasons for this can be attributed to his focus on other regions, geographical barriers, the lack of significant wealth and resources, and the lack of strategic importance of India at that time.